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book = Da Jilu |title = 大记录 Band 1 (中文) |prev = Da_Jilu |next = Da_Jilu/zh/Band_2 }}	Li Bingyin ed.
= 大记录 — 卷一 = 卷一 — Prolog, Die Goldbach-Vermutung, Kapitän, Leidenschaft, Chinesische Mädchen, u.a.	The Great Report
----	China's Reform and Opening 40 Years
序	A Selection of Reportage Literature
李炳银	Vol. I/V
2018年,是纪念中国自1978年开始的改革开放四十年的重要时日。四十年 来,中国在改革开放的道路上坚定不移,稳步深入,成果巨大,书写了中国社会历史 的新的辉煌篇章。2017年10月18日,习近平总书记在中国共产党第十九次全国 代表大会上的报告中指出:经过长期努力,中国特色社会主义进入了新时代,这是 我国发展新的历史方位。	Li Bingyin (Hg.):
四十年来,龙行九州,风雨兼程;凤舞大地,踏铁留痕。中国的改革开放,从历 史的长河看,尽管还是ー个社会瞬间表现,但它给中国的社会历史留下非常重要的 痕迹。面对当今中国在各个方面的积极巨大变化和重大国际影响カ,面对这个被 认为是国家从站起来,到富起来,到即将走向强起来的壮伟局面,身在其中的人们 一定会有很多的感慨和欣慰!	The Great Report. China's Reform and Opening 40 Years. A Selection of Reportage Literature. Vol. I ; Bochum : Europ. Univ.-vlg. 2025
在中国改革开放四十年的历史道路上,始终都有报告文学的热情参与和助力。 报告文学既以自己独特的个性声音深情地呼唤改革开放的发展,也以自己的热情 表达书写改革开放的伟大成就,是与中国的改革开放历史道路和实践交融最为密 切、互动最为有力的文体文学表达。邓小平1983年10月12日在中共十二届三中 全会上的讲话中,就曾明确指出:“文学方面,近年来反映社会主义建设新生活的文 学作品多了一些,但是,能够振奋人民和青年的革命精神,推动他们勇敢献身于祖 国各个领域的建设和斗争,具有强大鼓舞力量的作品,除了报告文学方面比较多以 外,其他方面也有,可是不能说多。”（见《邓小平文选》,人民出版社1993年版第三 卷,“党在组织战线和思想战线上的迫切任务”）人们一定还记得,当徐迟的报告文 学《哥德巴赫猜想》在1978年第1期《人民文学》上发表之后,由于作者在当时那 个限制环境中,对于“文化大革命”委婉而明确的批判态度,对于陈景润作为ー个 知识分子在科学攻关过程中的勇敢、坚韧和痴迷、努力的态度行为的热情赞赏和肯 定,而被广大读者极大关注,一度出现“洛阳纸贵”的火热情形。此后徐迟的《生09874命 之树长绿》,黄宗英的《大雁情》,理由的《高山与平原》《痴情》等很多彰显知识的价 值和科学家、艺术家的美好生活追求及人格力量的报告文学,分明有力地反对此前 那种否定知识、贬损科学艺术的社会思潮和行为,促使社会迅速生成向正确和文明 道路前进的力量。这是报告文学对人民群众意愿和期望中国改革开放的表达,是 文学式的呼唤改革开放的先声!这些作品,像春风吹拂着大地,使人们的心灵和意 识有力地复苏。	ISBN 978-3-86515-230-5
在中国社会经历“文化大革命”的浩劫之后,当地下的烈火即将喷发,郁结在 人们心中的怨愤需要释放的时候,张书绅为张志新烈士鸣冤的《正气歌》,王晨、张 天来惋惜遇罗克短暂悲剧人生的《划破夜幕的陨星》,陶斯亮悲叹父亲陶铸冤屈命 运的《一封终于发出的信》,胡平为李九莲抱冤的《中国的眸子》,理由痛心一个上 海青年生命的《倒在玫瑰色的晨光中》,孟晓云哀伤青年钱宗仁坎坷曲折人生的 《胡杨泪》等不少动情书写此前生活中各种血泪苦难的作品,引起了很大的社会震 动,也为开始酝酿的社会反思和思想解放潮流提供了很大的支持。在中国社会处 于ー个重大的扭转、推进和改变的时候,中国的报告文学创作在传达和传递民众情 绪愿望、诉求的过程中,发挥了非常可贵的担当和引领作用。报告文学不负民众的 期待和历史的责任。以致今天,人们回想起报告文学在当时引起的社会震撼情形 时,依然十分激动!	ISBN: 978-3-869966-230-5, EAN: *9783865152305*
历史一定会有曲折,但历史也一定会遵循着自己的发展规律向前推进。在反 思和拨乱反正不断深入的时候,农村的巨大变革出现了。万里作为省委书记在安 徽的作为,为中国新的发展开辟了道路。王立新的《毛泽东以后的岁月》、李延国 的《中国农民大趋势》、乔迈的《三门李逸闻》、王兆军的《原野在呼唤》等很多作品, 真实地书写、报告了来自农村的新动态和动人的改革热潮情景。中国广大的农村 在自在生长中焕发出巨大的力量,在创造着神奇的勃发景象。新的社会环境带来 新的变化,也会带来新的社会问题,刘宾雁的《人妖之间》,张敏的《神圣忧思录》, 赵瑜的《强国梦》,胡平、张胜友的《世界大串连》,徐刚的《伐木者,醒来!》,卢跃刚 的《长江三峡:中国的史诗》,杨晓升的《只有一个孩子》,郭冬的《难回故里》等等, 很多反映真实的社会观察、疑惑、拷问、探究的报告文学出现了。这些在社会巨大 的改变面前让人感到欣慰和忧患的作品,是报告文学紧密伴随中国社会改革开放 前进脚步的表现,也是报告文学在中国的社会生活中积极探寻社会发展和改变的 实践活动。当将真诚的热情与冷峻的面对结合到ー起时,报告文学对社会的参与 进入了一个新的阶段,同样是追踪中国改革开放轨迹的健康运动。因为这些滋生 和成长于中国深厚土地上的报告文学的真实表达,中国社会变革的性格和面貌日 渐清晰与明朗,中国社会的内容也空前地丰富多彩了。	This is volume no. I. ISBN of all volumes: I: 978-3-86515-230-5, II: 978-3-86515-607-5, III: 978-3-86515-608-2, IV: 978-3-86515-609-9, V: 978-3-86515-610-5.
在思想的禁锢被打破,闭锁的国门被打开之后,中国的改革开放就渐渐地由拨 乱反正向以经济建设为中心上转移。报告文学是敏锐、自觉并最热情地贴近这个 中心的文体,也09874是在这个舞台上表现最为充分和精彩的文体。这样的精彩演出,至 今也不曾落幕。早先柯岩的《船长》,陈祖芬的《理论狂人》,周嘉俊的《步鑫生现象 的反思》,李士非的《热血男儿》,王宏甲的《智慧风暴》,贾宏图的《解冻》,杨守松的 《昆山之路》,王宏甲、刘建的《休息的革命》,及后来李春雷的《木棉花开》,陈锡添 的《东方风来满眼春》,张雅文的《4万:400万的牵挂》,朱晓军、李英的《让百姓做 主》,江永红的《好梦将圆时》等等,着眼社会改革开放和促进经济建设发展的报告 文学,都在当时给人们以强烈的感染,留下了清晰深刻的记忆。这些作品,书写国 家政策的调整,描绘改革人物智慧勇敢的创新精神、行为,探讨排除各种束缚艰难 的方法,找寻内外联系发展的途径,热情歌颂所有推动中国走向发展、富强和文明 的对象,是透视现实的强光。它们将改革开放的锣鼓,通过报告文学的书写方式, 敲打得更加响亮。以致报告文学自身的存在,也成为中国走向改革开放的ー种明 显标志。	Chinese Original: 《大记录——中国改革开放四十年报告文学选》李炳银 主编
伴随着中国改革开放脚步的伟大迈进,报告文学的价值在结合很多自豪光荣 的辉煌成果书写中得到彰显,从而成为中国改革开放的杰出伴随者和珍贵记录,报 告文学作家成为很多重大历史事件的见证者和发言人,他们的报告文学作品成为 四十年来中国社会历史内容的ー个特殊的组成部分。像长江的《香港回归祖国十 周年回眸》、何建明激情记述2011年中国从利比亚等战乱地区大规模撤侨情景的 《国家》、蒋巍动情描绘中国高速铁路从发展壮大到领先世界历程的《闪着泪光的 事业》、许晨传递中国深海潜水器“蛟龙号”研制试验并获得骄人成果的《蛟龙探 海》、兰宁远记录中国人飞天梦想和伟大实践的《“神舟”天路》、陈启文深情描绘袁 隆平在伟大的时代创造出“杂交水稻和超级稻”情景的《袁隆平的世界》、李青松简 洁描述中国无人机开发进程和喜人成果的《智慧之翼》等作品,就是记录中国在改 革开放年代创造出的辉煌成果的史志性作品,是中国建设发展和促进人类进步的 美好记忆的构成部分!	Copyright © 2018.10 安徽文艺出版社 Anhui Literature and Art Press
1982年,著名诗人和文学理论家、中国作家协会副主席张光年先生,在谈到中 国的报告文学的时候,曾说:报告文学“由附庸蔚为大国”,成为中国文学家族中独 立存在的重要文体成员。四十年来,中国的报告文学,伴世生长,驭风而行,坚定自 己的中国立场和文明目标,在深入现实对社会、人生进行观察、发现、思考和文学表 达的过程中,表现出了独特的个性风格和坚定的使命担当精神。报告文学这种既 吸收了新闻的真实性原则,又很好地借重文学艺术表达方式的个性文体,是在新闻 与虚构的文学中间地带发现、开辟的新的文学领地与活动舞台。在新闻媒体手段 多样和人们迫切渴望走近各种社会真相的当下,报告文学具有难以替代的现实需 要和力量。“真实是艺术的上等原料”,真实为一切有价值的表达提供了基础和可 能。那些出于传统保守的文学观念,以自视清高的态度,认为只有虚构オ可以实现 艺术目标的认识行为,是ー种偏执甚至无知的表现。像这些相对直接呼应着中国 改革开放历史生活的作品,是对真实社会生活发展进程的观察和思考记录,其本身 也已经成为中国四十年历史生活的重要一环。报告文学在社会伟大进程中所发挥 的积极作用,已经被人们充分认可。因此,报告文学在面对中国四十年改革开放历 史时不会感到汗颜,而会具有自豪和欣慰,有自我珍爱和敬惜之感。虽然报告文学 还存在着不少的遗憾,还有需要不断提高和改进的地方,但是,在纪念中国改革开 放四十年伟大历史的时候,报告文学完全可以骄傲地说:我无愧于这个伟大的 时代!	Translation: Martin Woesler 吴漠汀 (Hunan Normal Universität 湖南师范大学), Xiaoyu (Emily) Wang
2018年2月18日于北京	English Edition Copyright © European University Press, published December 2025
哥德巴赫猜想	All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as expressly permitted by law, without the prior written permission of the Publisher.
徐迟	Bibliographic Information published by the Deutsche Nationalbibliothek: The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available online at http://dnb.d-nb.de.
为革命钻研技术,分明是又红又专,被他们攻击为白专道路。，，	Translation and book were realized with Chinese state support. The content of the book does not express the opinion of European University Press or the translators. The book is a contemporary historical document of Chinese propaganda. It is made available for scholarly reception.
九七八年两报ー刊元旦社论《光明的中国》	This edition was published in 2025 by European University Press
-へ	Europäischer Universitätsverlag GmbH Berlin · Bochum · Dülmen · London · Paris 2025
命P,（l,2 ）为适合下列条件的素数p的个数:	Prologue
X -p = Pl 或 X -p = р^Рз	Li Bingyin
其中Pl,P2 ,P3都是素数。	2018 marked forty years since China initiated its reform and opening-up policy in 1978, a program that combined domestic economic restructuring with greater international engagement. Throughout these four decades, China has pursued this path with consistency, transforming its social and economic landscape while redefining its place in the global order. Indeed, in his report to the 19th National Congress of the Communist Party of China on October 18, 2017, General Secretary Xi Jinping observed that “after long-term efforts, socialism with Chinese characteristics has entered a new era, marking a new historic stage in the country's development.”
20〔这是不好懂的;读不懂时,可以跳过这几行。〕	In the vast river of history, this period of reform and opening may appear only as a brief moment, yet it has left deep and lasting traces across the nation. The imagery of “dragons soaring across the provinces and phoenixes dancing upon the land” captures the dynamism and vitality of these four transformative decades. Amid far-reaching transformations in every sphere of life and China's expanding role in the world, those living through this era have witnessed not only material progress but also a profound reconfiguration of social structures and collective aspirations, as the nation has moved from recovery to modernization and toward global influence.
用x表一充分大的偶数。	Throughout China's reform era, reportage literature has played an active role: it has not only voiced a passionate call for reform and opening but also documented its unfolding and achievements with distinctive intensity. Among all literary forms, it is the one most closely integrated with, and most powerfully interactive with, China's historical course since 1978. In his speech at the Third Plenary Session of the 12th Central Committee of the Communist Party of China on October 12, 1983, Deng Xiaoping observed: “In recent years, there have been more literary works depicting the new life of socialist construction. However, works capable of inspiring the revolutionary spirit of the people and the youth—encouraging them to dedicate themselves courageously to building and striving in various fields of the motherland—remain relatively few. Among these, reportage literature contains comparatively more such works, though they are still not numerous overall.” (See Selected Works of Deng Xiaoping, Volume III, People's Publishing House, 1993 edition, “Urgent Tasks of the Party on the Organizational and Ideological Fronts.”)
命 C, = I l IИ （ ] - yr:亦）〇	Readers will also recall that when Xu Chi's reportage “Goldbach’s Conjecture” was published in the first issue of People's Literature in 1978, it attracted tremendous attention. Written during a restrictive era, the work combined a subtle yet unmistakable critique of the Cultural Revolution with an impassioned celebration of Chen Jingrun's courage, perseverance, and single-minded dedication to scientific research. Its reception was so overwhelming that it gave rise to what became known as the phenomenon of “Luoyang paper becoming expensive”—an idiom denoting a literary sensation that drives demand to extraordinary heights.
即 ハ・ р — 2.р>г （/—1）- °	This was followed by Xu Chi's “The Tree of Life Grows Green,” Huang Zongying's “Wild Goose Affection,” and Li You's “Infatuation,” along with many other works of the same genre. Collectively, these pieces stood in sharp contrast to the earlier social currents that had devalued knowledge and disparaged science and art, helping to reorient public consciousness toward intellectual pursuit and cultural renewal. In doing so, reportage literature gave voice to the people's aspirations for change—it became a literary expression that anticipated the coming reform era. Like a spring breeze sweeping across the land, these works revitalized the public spirit and reawakened social awareness.
对于任意给定的偶数h及充分大的ル,用も（1,2）表示满足下面条件的素 数p的个数:	After Chinese society endured the catastrophe of the Cultural Revolution—when underground fires were about to erupt and the resentment long held in people's hearts demanded release—works such as Zhang Shengshu's “Song of Righteousness,” written in defense of the martyr Zhang Zhixin; Wang Chen and Zhang Tianlai's “Meteor Piercing the Night,” lamenting the brief and tragic life of Yu Luoke; Tao Siliang's sorrowful letter on her father Tao Zhu's wrongful fate in “A Letter Finally Sent”; Hu Ping's protest for Li Jiulian in “China's Eyes”; Li You's account of a Shanghai youth's heartbreak in “Falling in the Rosy Dawn”; and Meng Xiaoyun's mourning of young Qian Zongren's painful life in “Tears of the Populus Euphratica”—together with many other emotionally charged writings about past suffering—struck a powerful chord.
pWx,p +h = pi 或 h + p = P2P3,	These works provoked significant resonance and powerfully supported the emerging currents of social reflection and ideological liberation. At a moment when Chinese society stood at a major turning point—moving forward and undergoing profound transformation—reportage literature played a crucial role in articulating public emotion, hope, and collective aspiration. It met the expectations placed upon it and lived up to the weight of its historical responsibility. Even today, when readers recall the influence and impact of reportage literature during that period, they remain deeply moved.
其中Pi ,Ра ,Рз都是素数。	History inevitably advances through both setbacks and progression, yet it unfolds according to its own internal logic. As reflection and reform deepened, tremendous changes began to take shape in the countryside. Wan Li's initiatives as Party Secretary in Anhui opened new paths for China's development. Works such as Wang Lixin's “Years After Mao Zedong,” Li Yanguo's “The Great Trend of Chinese Farmers,” Qiao Mai's “Anecdotes of Sanmen Li,” and Wang Zhaojun's “The Wilderness Calls,” among many others, faithfully chronicled new developments in rural life and the fervor of reform. China's vast countryside burst with renewed vitality, its spontaneous energy giving rise to scenes of remarkable dynamism. Yet these new social conditions brought not only revitalization but also fresh challenges.
本文的目的在于证明并改进作者在文献〔1〇〕内所提及的全部结果,现在 详述如下。	In response, a wave of reportage works emerged: Liu Binyan's “Between Man and Monster,” Zhang Min's “A Record of Sacred Sorrows,” Zhao Yu's “Dreams of a Strong Nation,” Hu Ping and Zhang Shengyou's “World Grand Connection,” Xu Gang's “Wake Up, Lumberjacks!,” Lu Yuegang's “Yangtze Three Gorges: China's Epic,” Yang Xiaosheng's “Only One Child,” Guo Dong's “Difficult Homecoming,” and many others that engaged in observing, questioning, and exploring contemporary society. These works, which left readers both reassured and uneasy in the face of rapid change, demonstrated reportage literature's role in closely accompanying the forward movement of China's reform era. They also marked reportage's active engagement in examining the nation's social development and transformation.
II	When heartfelt enthusiasm was joined with a sober reckoning with reality, reportage literature's engagement with society entered a new stage—one that evolved in tandem with the nation's ongoing transformation. Through these truthful depictions rooted in Chinese life, the contours of social change became increasingly distinct, and the texture of society grew richer and more complex than ever before.
以上引自ー篇解析数论的论文。这一段引自它的“（一）引言”,提出了这道 题。它后面是“（二）几个引理”,充满了各种公式和计算。最后是“（三）结果”,证 明了一条定理。这篇论文,极不好懂。即使是著名数学家,如果不是专门研究这ー 个数学的分支的,也不一定能读懂。但是这篇论文已经得到了国际数学界的公认, 誉满天下。它所证明的那条定理,现在世界各国一致地把它命名为“陈氏定理”， 因为它的作者姓陈,名景润。他现在是中国科学院数学研究所的研究员。	After the shackles on thought were broken and the country's closed doors opened, China's national agenda gradually shifted from restoring order to prioritizing economic modernization. Reportage literature proved to be the genre most attuned, most self-aware, and most intimately connected with this new orientation—and it performed most vividly and convincingly on this stage. Such achievements have continued to the present day.
陈景润是福建人,生于ー九三三年。当他降生到这个现实人间时,他的家庭和 社会生活并没有对他呈现出玫瑰花朵一般的艳丽色彩。他父亲是邮政局职员,老 是跑来跑去的。当年如果参加了国民党,就可以飞黄腾达,但是他父亲不肯参加。 有的同事说他真是不识时务。他母亲是ー个善良的操劳过甚的妇女,ー共生了十 二个孩子,只活了六个,其中陈景润排行老三。上有哥哥和姐姐,下有弟弟和妹妹。 孩子生得多了,就不是双亲所疼爱的儿女了。他们越来越成为父母的累赘一多 余的孩子,多余的人。从生下来的那一天起,他就像ー个被宣布为不受欢迎的人似 的,来到了这人世间。	Earlier works such as Ke Yan's “The Captain,” Chen Zufen's “Theory Fanatic,” Zhou Jiajun's “Reflections on the Bu Xinsheng Phenomenon,” Li Shifei's “Hot-Blooded Men,” Wang Hongjia's “Wisdom Storm,” Jia Hongtu's “Thaw,” Yang Shousong's “The Kunshan Road,” and Wang Hongjia and Liu Jian's “The Revolution of Rest”—together with later pieces like Li Chunlei's “Kapok Blossoms,” Chen Xitian's “Spring Arrives on the Eastern Wind,” Zhang Yawen's “The Concern Between 40,000 and 4 Million,” Zhu Xiaojun and Li Ying's “Let the People Be Masters,” and Jiang Yonghong's “When Good Dreams Come True”—all focused on the social transformations and economic dynamism of the new era. These works offered readers powerful inspiration at the time and left enduring, profound impressions upon society.
他甚至没有享受过多少童年的快乐。母亲劳苦终日,顾不上爱他。当他记事 的时候,酷烈的战争爆发。日本鬼子打进福建省。他还这么小,就提心吊胆过生 活。父亲到三元县的三明市一个邮政分局当局长。小小邮局,设在山区一座古寺 庙里。这地方曾经是ー个革命根据地。但那时候,茂郁山林已成为悲惨世界。所 有男子汉都被国民党匪军疯狂屠杀,无一幸存者。连老年的男人也一个都不剩了 〇 剩下的只有妇女,她们的生活特别凄凉。花纱布价钱又太贵了,穿不起衣服,大姑 娘都还裸着上体。福州被敌人占领后,逃难进山来的人多起来。这里飞机不来轰 炸,山区渐渐有点儿兴旺。却又迁来了一个集中营。深夜里,常有鞭声惨痛地回 荡;不时还有杀害烈士的枪声。第二天,那些戴着镣铐出来劳动的人,神色就更阴 森了。	These works addressed national policy adjustments, portrayed the wisdom and bravery of figures during this era, explored ways to overcome restrictive obstacles, sought paths to connect internal reform with external development, and praised all forces that contributed to China's progress toward prosperity and strength. They shone as beams of light piercing reality, and through reportage literature's unique narrative power, they made the drums of reform echo ever louder. The very existence of reportage literature came to stand as an unmistakable symbol of China's reform era.
陈景润的幼小心灵受到了极大的创伤。他时常被惊慌和迷惘所征服。在家里 并没有得到乐趣,在小学里他总是受人欺侮。他觉得自己是ー只丑小鸭。不,是 人,他还是觉得自己也是一个人。只是他瘦削、弱小。光是这副窝囊样子就不能讨 人喜欢。习惯于挨打,从来不讨饶,这更使对方狠狠揍他,而他则更坚韧而有耐力 了。他过分敏感,过早地感觉到了旧社会那些人吃人的现象。他被造成了一个内 向的人,内向的性格。他独独爱上了数学。不是因为被迫,他只是因为爱好数学, 演算数学习题占去了他大部分的时间。	Accompanying the great strides China took since 1978, reportage literature demonstrated its value by recording remarkable achievements, becoming a precious chronicle of national transformation. Reportage writers served as witnesses and spokespersons for many major historical events, and their works became an integral part of forty years of China's social history.
当他升入初中的时候,江苏学院从远方的沦陷区搬迁到这个山区来了。那学 院里的教授和讲师也到本地初中里来兼点课,多少也能给他们流亡在异地的生活 改善一些。这些老师很有学问。有个语文老师水平最高。大家都崇拜他。但陈景 润不喜欢语文。他喜欢两个外地的数理老师。外地老师倒也喜欢他。这些老师经 常吹什么科学救国ー类的话。他不相信科学能救国,但是救国却不可以没有科学, 尤其不可以没有数学,而且数学是什么事儿也少不了它的。人们对他歧视,拳打脚 踢,只能使他更加爱上数学。枯燥无味的代数方程式却使他充满了幸福,成为唯一 的乐趣。	Further examples include Chang Jiang's “Hong Kong’s Return to the Motherland: A 10-Year Retrospective”; He Jianming's “Nation,” a passionate account of China's large-scale evacuation of citizens from Libya and other war-torn regions in 2011; Jiang Wei's “A Career Accompanied by Tears,” a moving depiction of China's high-speed rail development from its beginnings to global leadership; Xu Chen's “The Dragon Explores the Sea,” on the achievements of deep-sea submersible research and testing; Lan Ningyuan's “The ‘Shenzhou’ Highway to Heaven,” recording the people's dream and practice of spaceflight; Chen Qiwen's “Yuan Longping's World,” an affectionate portrayal of the scientist's creation of hybrid rice and other high-yield varieties; and Li Qingsong's “Wings of Wisdom,” a concise account of the development and achievements of unmanned aircraft. Together with many others, these works stand as historical chronicles of the extraordinary accomplishments China has achieved.
十三岁那年,他母亲去世了,死于肺结核。从此,儿想亲娘在梦中,而父亲又结 了婚,后娘对他就更不如亲娘了。抗战胜利了,他们回到福州。陈景润进了三一中 学,毕业后又到英华书院去念高中。那里有个数学老师,曾经是清华大学的航空系 主任。	The works collected in this volume capture the remarkable transformations China experienced during the reform era, preserving them as part of the nation's collective memory and its contribution to global progress.
III	In 1982, the poet and literary theorist Zhang Guangnian—then Vice Chairman of the Chinese Writers Association—remarked that reportage literature had “grown from dependency to become a great power,” emerging as an independent and influential genre within modern Chinese writing. Over the past four decades, it has evolved in step with the times, riding the winds of change while simultaneously upholding its national perspective and cultural ideals. Through its deep observation, critical reflection, and artistic rendering of society and everyday life, reportage literature has developed a distinctive aesthetic and a profound level of social responsibility.
老师知识渊博,又诲人不倦。他在数学课上,给同学们讲了许多有趣的数学知 识。不爱数学的同学都能被他吸引住,爱数学的同学就更不用说了。	As a genre that unites journalism's commitment to truth with the imaginative depth of fiction, reportage literature opened new ground, creating a distinct space of intersection between factual narrative and artistic expression. In today's media-saturated world—where readers continue to seek authentic representations of social reality—reportage retains a unique and enduring power. “Truth is art's greatest source of raw material”: it provides both the foundation and the possibility of meaningful creation. Conversely, those who, clinging to conservative literary hierarchies, maintain that only fiction can achieve artistic merit, expose a narrow understanding of art and its capacities. Works that reflect China's historical transformation since the late 1970s serve as both observation and record, capturing the realities of social development and becoming an integral part of the nation's modern history. The constructive role that reportage literature has played in this process has been widely acknowledged. Looking back on the past four decades, the genre can take justifiable pride in its contributions, grounded in a strong sense of social responsibility and artistic purpose. Although it still faces limitations and room for further growth, in commemorating these decades of profound change, reportage literature may rightfully affirm its enduring relevance and worth to this transformative era!
数学分两大部分:纯数学和应用数学。纯数学处理数的关系与空间形式。在 处理数的关系这部分里,讨论整数性质的ー个重要分支,名叫“数论” 〇十七世纪 法国大数学家费马是西方数论的创始人。但是中国古代老早已对数论做出了特殊 贡献。《周髀》是最古老的古典数学著作。较早的还有一部《孙子算经》。其中有 一条余数定理是中国首创。后来被传到了西方,名为孙子定理,是数论中的一条著 名定理。直到明代以前,中国在数论方面是对人类有过较大的贡献的。五世纪的 祖冲之算出来的圆周率,比德国人叫奥托的,早出一千多年。约瑟夫（指斯大林） 领导的科学家把月球的ー个山谷命名为“祖冲之”。十三世纪下半纪更是中国古 代数学的高潮。南宋大数学家秦九韶著有《数书九章》。他的联立一次方程式的 解法比意大利大数学家欧拉的解法早出了五百多年。元代大数学家朱世杰,著有 《四元玉鉴》。他的多元高次方程的解法,比法国大数学家毕朱,也早出了四百多 年。明清以后,中国落后了。然而中国人对于数学好像是特具禀赋的。中国应当 出大数学家。中国是数学的好温床。	February 18, 2018, Beijing
有一次,老师给这些高中生讲了数论之中一道著名的难题。他说,当初,俄罗 斯的彼得大帝建设圣彼得堡,聘请了一大批欧洲的大科学家。其中,有瑞士大数学 家欧拉（他的著作共有八百余种）;还有德国的一位中学教师,名叫哥德巴赫,也是 数学家。	Table of Contents
一七四二年,哥德巴赫发现,每ー个大偶数都可以写成两个素数的和。他对许 多偶数进行了检验,都说明这是确实的。但是这需要给予证明。因为尚未经过证 明,只能称为猜想。他自己却不能够证明它,就写信请教那赫赫有名的大数学家欧 拉,请他来帮忙做出证明。一直到死,欧拉也不能证明它。从此这成了一道难题, 吸引了成千上万数学家的注意。两百多年来,多少数学家企图给这个猜想做出证 明,都没有成功。	Volume I
说到这里,教室里成了开了锅的水。那些像初放的花朵ー样的青年学生叽叽 喳喳地议论起来了。	Preface, Li Bingyin 1
老师又说,自然科学的皇后是数学。数学的皇冠是数论。哥德巴赫猜想,则是 皇冠上的明珠。	Goldbach’s Conjecture, Xu Chi 9
同学们都惊讶地瞪大了眼睛。	The Captain, Ke Yan 36
老师说,你们都知道偶数和奇数,也都知道素数和合数。我们小学三年级就教 这些了。这不是最容易的吗?不,这道难题是最难的呢。这道题很难很难。要有 谁能够做了出来,不得了,那可不得了啊!	Infatuation, Li You 60
青年人又吵起来了。这有什么不得了。我们来做。我们做得出来。他们夸下 了海口。	Chinese Girls, Lu Guang 119
老师也笑了。他说:“真的,昨天晚上我还做了一个梦呢。我梦见你们中间有 一位同学,他不得了,他证明了哥德巴赫猜想。”	Anecdotes of Sanmen Li, Qiao Mai 181
高中生们轰的一声大笑了。	Tears of the Populus Euphratica, Meng Xiaoyun 195
但是陈景润没有笑。他也被老师的话震动了,但是他不能笑。如果他笑了,还 会有同学用白眼瞪他的。自从升入高中以后,他越发孤独了。同学们嫌他古怪,嫌 他脏,嫌他多病的样子,都不理睬他。他们用蔑视的和讥讽的眼神瞅着他。他成了 ー个踽踽独行,形单影只,自言自语,孤苦伶仃的畸零人。长空里,ー只孤雁。	The Wilderness Calls, Wang Zhaojun 212
第二天,又上课了。几个相当用功的学生兴冲冲地给老师送上了几个答题的 卷子。他们说,他们已经做出来了,能够证明那个德国人的猜想了,可以多方面地 证明它呢。没有什么了不起的。哈!哈!	Hot-Blooded Men, Li Shifei 233
“你们算了「’老师笑着说,“算了!算了!”	Volume II
“我们算了,算了。我们算出来了!”	The Great Trend of Chinese Farmers, Li Yanguo 3
“你们算啦！好啦好啦,我是说,你们算了吧,白费这个カ气做什么?你们这些 卷子我是看也不会看的,用不着看的。那么容易吗?你们是想骑着自行车到月球 上去。”	Theory Fanatic, Chen Zufen 57
教室里又爆发出ー阵哄堂大笑。那些没有交卷的同学都笑话那几个交了卷 的。他们自己也笑了起来,都笑得跺脚,笑破肚子了。唯独陈景润没有笑。他紧结 着眉头。他被排除在这一切欢乐之外。	A Record of Sacred Sorrows, Zhang Min 84
第二年,老师又回清华去了。他是北京航空学院副院长,全国航空学会理事长 沈元。他早该忘记这两堂数学课了。他怎能知道他被多么深刻地铭刻在学生陈景 润的记忆中。老师因为学生多,容易忘记,学生却常常记着自己青年时代的老师。	Dreams of a Strong Nation, Zhao Yu 124
四	Wake Up, Lumberjacks!, Xu Gang 179
福州解放!那年他高中三年级。因为交不起学费,ー九五〇年上半年,他没有 上学,在家自学了一个学期。高中没有毕业,但以同等学力报考,他考进了厦门大 学。那年,大学里只有数学物理系。读大学二年级时,オ有了一个数学组,但只有 四个学生。到三年级时,有数学系了,系里还是这四个人。因为成绩特别优异,国 家又急需培养人才,四个人提前毕了业;而且,立即分配了工作,得到的优待,羡慕 煞人。ー九五三年秋季,陈景润被分配到了北京!在第X中学当数学老师。这该 是多么的幸福了啊！	Reflections on the Bu Xinsheng Phenomenon, Zhou Jiajun 227
然而,不然！在厦门大学的时候,他的日子是好过的。同组同系就只四个大学 生,倒有四个教授和一个助教指导学习。他是多么饥渴而且贪婪地吸饮于百花丛 中,以酿制芬芳馥郁的数学蜜糖啊！学习的成效非常之高。他在抽象的领域里驰 骋得多么自由自在！大家有共同的dx和dy等等之类的数学语言。心心相印,息 息相通。三年中间,没有人歧视他,也不受骂挨打了。他很少和人来往,过的是黄 金岁月;全身心沉浸在数学的海洋里面。真想不到,那么快,他就毕业了。ー想到 他将要当老师,在讲台上站立,被几十对锐利而机灵,有时难免要被恶作剧的眼睛 盯视,他禁不住吓得打战！	Volume III
他的猜想立刻就得到了证明。他是完全不适合于当老师的。他那么瘦小和病 弱,他的学生却都是高大而且健壮的。他最不善于说话,多说几句就嗓子发痛了。 他多么羡慕那些循循善诱的好老师。下了课回到房间里,他叫自己笨蛋。辱骂自 己比别人的还厉害得多。他一向不会照顾自己,又不注意营养。积忧成疾,发烧到 摄氏三十八度。送进医院ー检查,他患有肺结核和腹膜结核症。	The Kunshan Path, Yang Shousong 3
这一年内,他住医院六次,做了三次手术。当然他没有能够好好地教书。但他 并没有放弃了他的专业。中国科学院不久前出版了华罗庚的名著《堆垒素数论》。 刚摆上书店的书架,陈景润就买到了。他ー头扎进去了。非常深刻的著作,非常之 艰难！可是他钻研了它。住进医院,他还偷偷地避开了医生和护士的耳目,研究 它。他那时也认为,这样下去,学校没有理由欢迎他。	Flying to the Space Port, Li Mingsheng 52
他想他也许会失业?又有什么办法呢?好在他节衣缩食,ー只牙刷也不买。 他从来不随便花一分钱,他几乎积蓄了他的全部收入。他横下心来,失业就回家, 还继续搞他的数学研究。积蓄这几个钱是他搞数学的保证。这保证他失了业也还 能研究数学的几个钱,就是他的生命:他的生命就是数学。至于积蓄一旦用光了, 以后呢?他不知道。那时又该怎么办?这也是难题,也是尚未得到解答的猜想。 而这个猜想后来也被证明是猜对了的。他的病好不了,中学里后来无法续聘他了。	Spring Arrives on the Eastern Wind, Chen Xitian 123
厦门大学校长来到了北京,在教育部开会。那中学的一位领导遇见了他,谈起 来,很不满意,提出了一大堆的意见:你们怎么培养了这样的高オ生?	When Good Dreams Come True, Jiang Yonghong 171
王亚南,厦门大学校长,就是马克思的《资本论》的翻译者,听到意见之后,非 常吃惊。他一直认为陈景润是他们学校里最好的学生。他不同意他所听到的意 见。他认为这是分配学生的工作时,分配不得当。他同意让陈景润回到厦门大学。	Wisdom Storm, Wang Hongjia 3
听说他可以回厦门大学数学系了,说也奇怪,陈景润的病也就好转了。而王亚 南却安排他在厦大图书馆当管理员。又不让管理图书,只让他专心致志地研究数 学。王亚南不愧为政治经济学的批判家,他懂得价值论,懂得人的价值。陈景润也 没有辜负了老校长的培养。他果然精深地钻研了华罗庚的《堆垒素数论》和大厚 本儿的《数论导引》。陈景润都把它们吃透了。他的这种经历却也并不是没有先 例的。	Volume IV
当初,我国老ー辈的大数学家、大教育家熊庆来,我国现代数学的引进者,在北 京的清华大学执教。三十年代之初,有一个在初中毕业以后就失了学,失了学就完 全自学的青年人,寄出了一篇代数方程解法的文章,给了熊庆来。熊庆来ー看,就 看出了这篇文章中的英姿勃发和奇光异彩。他立刻把它的作者,姓华名罗庚的,请 进了清华园来。他安排华罗庚在清华数学系当文书,可以一面自学,一面大量地听 课。尔后,派遣华罗庚出国,留学英国剑桥。学成回国,已担任在昆明的云南大学 校长的熊庆来又介绍他当联大教授。华罗庚后来再次出国,在美国普林斯顿和依 利诺的大学教书。中华人民共和国成立以后,华罗庚马上回国来了,他主持了中国 科学院数学研究所的工作。	The Concern Between 40,000 and 4 Million, Zhang Yawen 3
陈景润在厦门大学图书馆中也很快写出了数论方面的专题文章,文章寄给了 中国科学院数学研究所。华罗庚一看文章,就看出了文章中的英姿勃发和奇光异 彩,也提出了建议,把陈景润选调到数学研究所来当实习研究员。正是:熊庆来慧 眼认罗庚,华罗庚睿目识景润。	Hong Kong’s Return to the Motherland: A 10-Year Retrospective, Chang Jiang 58
ー九五六年年底,陈景润再次从南方海滨来到了首都北京。	Kapok Blossoms, Li Chunlei 85
ー九五七年夏天,数学大师熊庆来也从国外重返祖国首都。这时少长咸集,群 贤毕至。当时著名的数学家有熊庆来、华罗庚、张宗燧、闵嗣鹤、吴文俊等等许多明 星灿灿;还有新起的一代俊彦,陆启铿、万哲先、王元、越民义、吴方等等,如朝霞烂 漫;还有后起之秀,陆汝铃、杨乐、张广厚等等已入北京大学求学。在解析数论、代 数数论、函数论、泛函分析、几何拓扑学等等的学科之中,已是人才济济,又加上了 ー个陈景润。人人握灵蛇之珠,家家抱荆山之玉。风靡云蒸,阵容齐整。条件具备 了,华罗庚做出了部署:侧重于应用数学,但也要向那皇冠上的明珠,哥德巴赫猜想 挺进!	The Revolution of Rest, Wang Hongjia and Liu Jian 111
五	A Career Accompanied by Tears, Jiang Wei 162
要懂得哥德巴赫猜想是怎么一回事,只需把早先在小学三年级里就学到过的 数学再来温习一下。那些12345,个十百千万的数字,叫作正整数。那些可以被2 整除的数,叫作偶数。剩下的那些数,叫作奇数。还有一种数,如2,3,5,7,11,13 等等,只能被1和它本数,而不能被别的整数整除的,叫作素数。除了 1和它本数 以外,还能被别的整数整除的,这种数如4,6,8,9,10,12等等就叫作合数。ー个整 数,如能被ー个素数所整除,这个素数就叫作这个整数的素因子。如6,就有2和3 两个素因子。如30,就有2,3和5三个素因子。好了,这暂时也就够用了。	Difficult Homecoming, Guo Dong 187
一七四二年,哥德巴赫写信给欧拉时,提出了:每个不小于6的偶数都是两个 素数之和。例如,6=3+3。又如,24 = 11+13等等。有人对ー个ー个的偶数都进 行了这样的验算,一直验算到了三亿三千万之数,都表明这是对的。但是更大的数 目,更大更大的数目呢?猜想起来也该是对的。猜想应当证明。要证明它却很难 很难。	Volume V
整个十八世纪没有人能证明它。	Nation, He Jianming 3
整个十九世纪也没有人能证明它。	The Dragon Explores the Sea, Xu Chen 86
到了二十世纪的二十年代,问题オ开始有了点儿进展。	Yuan Longping’s World, Chen Qiwen 135
很早以前,人们就想证明,每ー个大偶数是两个“素因子不太多的”数之和。 他们想这样子来设置包围圈,想由此来逐步、逐步证明哥德巴赫这个命题ー个素数 加一个素数（1 +1）是正确的。	The “Shenzhou” Highway to Heaven, Lan Ningyuan 211
一九二〇年,挪威数学家布朗,用ー种古老的筛法（这是研究数论的ー种方 法）证明了:每ー个大偶数是两个“素因子都不超九个的”数之和。布朗证明了:九 个素因子之积加九个素因子之积（9 +9）,是正确的。这是用了筛法取得的成果。 但这样的包围圈还很大,要逐步缩小之。果然,包围圈逐步地缩小了。	Wings of Wisdom, Li Qingsong 254
一九二四年,数学家拉德马哈尔证明了（ 7 +7 ）；一九三二年,数学家爱斯斯尔	Appendix: Outstanding Reportage Literature from Forty Years of Reform and Opening-Up 272
曼证明了（6 +6）； 一九三八年,数学家布赫斯塔勃证明了（ 5 +5）； 一九四〇年,他 又证明了（4 +4）； 一九五六年,数学家维诺格拉多夫证明了（ 3 +3 ）； 一九五八年, 我国数学家王元又证明了（2+3 ）。包围圈越来越小,越接近于（1+1 ） 了。但是, 以上所有证明都有一个弱点,就是其中的两个数没有一个是可以肯定为素数的。	Goldbach's Conjecture
早在ー九四八年,匈牙利数学家兰恩易另外设置了一个包围圈。开辟了另ー 战场,想来证明:每个大偶数都是ー个素数和一个“素因子都不超过六个的”数之 和。他果然证明了（1 +6）。	Xu Chi
但是,以后又是十年没有进展。	“Those who study technology with revolutionary dedication are clearly both red and expert, yet they are criticized for following the so-called ‘white expert’ path.”
ー九六二年,我国数学家、山东大学讲师潘承洞证明了（1 +5 ）,前进了一步; 同年,王元、潘承洞又证明了 （ 1 +4）。ー九六五年,布赫斯塔勃、维诺格拉多夫和 数学家庞皮艾黎都证明了（1+3 ）。	— New Year’s editorial “Bright China,” Two Papers and One Journal, 1978
ー九六六年五月,ー颗璀璨的信号弹升上了数学的天空,陈景润在中国科学院 的刊物《科学通报》第十七期上宣布他已经证明了（1 +2） 〇	[Here, “red and expert” (you hong you zhuan) was a Mao-era slogan meaning both politically loyal and technically skilled; “white expert” (bai zhuan) was a derogatory label for those seen as valuing technical expertise while neglecting political commitment.]
自从陈景润被选调到数学研究所以来,他的才智的舊蕾ー朵朵地烂漫开放了。 在圆内整点问题、球内整点问题、华林问题、三维除数问题等等之上,他都改进了中 外数学家的结果。单是这ー些成果,他那贡献就已经很大了。	I
但当他已具备了充分依据,他就以惊人的顽强毅カ,来向哥德巴赫猜想挺进 了。他废寝忘食,昼夜不舍,潜心思考,探测精蕴,进行了大量的运算。ー心一意地 搞数学,搞得他发呆了。有一次,自己撞在树上,还问是谁撞了他。他把全部心智 和理性统统奉献在这道难题的解题上了,他为此而付出了很高的代价。他的两眼 深深凹陷了。他的面颊带上了肺结核的红晕。喉头炎严重,他咳嗽不停。腹胀、腹 痛,难以忍受。有时已人事不知了,却还记挂着数字和符号。他跋涉在数学的崎岖 山路,吃カ地迈动步伐。在抽象思维的高原,他向陡峭的媛岩升登,降下又升登! 善意的误会飞入了他的眼帘。无知的嘲讽钻进了他的耳道,他不屑ー顾,他未予理 睬。他没有时间来分辩,他宁可含垢忍辱。餐霜饮雪,走上去ー步就是ー步!他气 喘不已,汗如雨下。时常感到他支持不下去了。但他还是攀登。用四肢,用指爪。 真是艰苦卓绝！多少次上去了摔下来。就是铁鞋,也早该踏破了。人们嘲笑他穿 的鞋是破了的:硬是通风透气不会得脚气病的一双鞋子。不知多少次发生了可怕 的滑坠！几乎粉身碎骨。他无法统计他失败了多少次。他毫不气馁。他总结失败 的教训,把失败接起来,焊上去,作登山用的尼龙绳子和金属梯子。吃ー堑,长一 智。失败一次,前进ー步。失败是成功之母,成功由失败堆垒而成。他越过了雪 线,到达雪峰和现代冰川,更感缺氧的严重了。多少次坚冰封山,多少次雪崩掩埋! 他就像那些征服珠穆朗玛峰的英雄登山运动员,爬啊,爬啊,爬啊!而恶毒的诽谤, 恶意的污蔑像变天的乌云和九级狂风。然而热情的支持为他拨开云雾,爱护的阳 光又温暖了他。他向着目标,不屈不挠;继续前进,继续攀登。战胜了第一台阶的 难以登上的峻峭,出现在难上加难的第二台阶绝壁之前。他只知攀登,在千仞深渊 之上;他只管攀登,在无限风光之间。ー张又一张的运算稿纸,像漫天大雪似的飞 舞,铺满了大地。数字、符号、引理、公式、逻辑、推理,积在楼板上,有三尺深。忽然 化为膝下群山,雪莲万千。他终于登上了攀登顶峰的必由之路,登上了（ 1 +2）的 台阶。	Let P₁(1, 2) be the number of primes p satisfying the following conditions:
他证明了这个命题,写出了厚达二百多页的长篇论文。	x - p = p₁ or x - p =p₂p₃
闵嗣鹤老师给他细心地阅读了论文原稿。检查了又检查,核对了又核对。肯 定了,他的证明是正确的,靠得住的。他给陈景润说,去年人家证明（1 +3）是用了 大型的、高速的电子计算机。而你证明（1+2 ）却完全靠你自己运算。难怪论文写 得长了。太长了,建议他加以简化。	where p₁, p₂, p₃ are all primes. [This passage may be challenging to understand; if necessary, you may omit these lines on a first reading.]
本文第一段最后一句说到的“文献〔!〇〕”就是这时他以简报形式,在《科学通 报》上宣布的,但只提到了结果,尚未公布他的证明。他当时正修改他的长篇论文。 就是在这个当口,突然陈景润被卷入了政治革命的万丈波澜。滚滚而来的巨浪冲 击了一切剥削阶级的思想意识。史无前例的无产阶级“文化大革命”,像颗颗的精 神原子弹氢弹的成功试验ー样,在神州大地上连续爆炸了。	Let x be a sufficiently large even number where the following can be defined:
六	For any given even number h and sufficiently large X, let φ(1,2) represent the number of primes p satisfying the following conditions:
无产阶级发动的“文化大革命”也是政治大革命。人类历史上从来没有过这 样伟大的群众运动。整个人类的四分之一,不分男女老少,齐动员起来。壮丽的大 革命,把エ、农、兵,劳动群众和知识分子,还有圣徒和魔鬼,ー股脑儿卷了进去。检 举和被检举,揭发和被揭发,批评和反批评,批判和自我批判。	p ≤ x, p + h = p₁ or h + p = P₂P₃, where P₁, P₂, P₃ are all primes.
中国发生了“内战”。到处是有组织的激动,有领导的对战,有秩序的混乱。 无产阶级的革命就是经常自己批判自己。一次一次地胜利;一次一次地反复。把 仿佛已经完成的事情,一次一次的重新来过,把这些事情再做一遍,每一次都有了 新的提高。它搜索自己的弱点、缺点和错误,毫不留情。像马克思说过的要让敌人 更加强壮起来,自己则再三往后退却,直到无路可退了,オ作罗陀斯岛上的跳跃;粉 碎了敌人,再在玫瑰园里庆功。只见ー个ー个的场景,闪来闪去,风驰电掣,惊天动 地。一台一台的戏剧,排演出来,喜怒哀乐,淋漓尽致;悲欢离合,动人心肺。ー个 ー个的人物,登上场了。有的折戟沉沙,死有余辜;四大家族,红楼ー梦;有的昙花 ー现,萎谢得好快啊。乃有青松翠柏,虽死犹生,重于泰山,浩气长存!有的是国杰 豪英,人杰地灵;干将莫邪,千锤百炼;拂钟无声,削铁如泥。ー页ー页的历史写出 来了,大是大非,终于有了无私的公论。肯定一否定一否定之否定。化妆不经 久要剥落,被诬的终究要昭雪。种子播下去,就有收获的一天。播什么,收什么。	The purpose of this paper is to prove and improve all the results mentioned by the author in reference [10], now detailed as follows.
天文地理要审查,物理化学要审查,生物要审查,数学也要审查。陈景润在无 产阶级文化大革命中受到了最严峻的考验。老ー辈的数学家受到了冲击,连中年 和年轻的也跑不了。庄严的科学院被骚扰了,热腾腾的实验室冷清清了。日夜的 辩论,剧烈的争吵。行动胜于语言,拳头代替舌头。无产阶级“文化大革命”像ー 个筛子,什么都要在这筛子上过滤一下。它用的也是筛法。该筛掉的最后都要筛 掉,不该筛掉的怎么也筛不掉。	II
曾经有人强调了科学工作者要安心工作,钻研学问,迷于专业。陈景润又被认 为是这种所谓资产阶级科研路线的“安钻迷”典型。确实他成天钻研学问。不关 心政治,是的,但也参加了历次的政治运动。共产党好,国民党坏,这个朴素的道理 他非常之分明。数学家的逻辑像钢铁ー样坚硬;他的立场站得稳。他没有犯过什 么错误。在政治历史上,陈景润一身清白。他白得像ー只仙鹤。鹤羽上,污点沾不 上去;而鹤顶鲜红;两眼也是鲜红的,这大约是他熬夜熬出来的。他曾下厂劳动,也 曾用数学来为生产服务,尽管他是从事于数论这一基础理论科学的。但不关心政 治,最后政治要来关心他。并且,要狠狠地批评他了。批评得轻了,不足以触动他。 只有触动了他,才能使他今后注意路线关心政治。批评不怕过分,矫枉必须过正。 但是,能不能一推就把他推过敌我界线?能不能将他推进“专政队”里去?尽量摆 脱外界的干扰,以专心搞科研又有何罪?	The passage quoted above is drawn from a paper in analytic number theory. It appears in Section (1), “Introduction,” where the central problem is outlined. The paper then proceeds to Section (2), “Several Lemmas,” which develops the necessary formulas and intermediate results, and concludes with Section (3), “Results,” where the main theorem is proved. The work is exceptionally challenging to understand; even accomplished mathematicians outside this specialization may find it difficult to follow. Nevertheless, it soon gained international recognition and became widely celebrated. The theorem it established has since become known worldwide as Chen's theorem, named after its author, Chen Jingrun, currently a researcher at the Institute of Mathematics, Chinese Academy of Sciences.
善意的误会,是容易纠正的;无知的嘲讽,也可以谅解的。批判ー个数学家,多 少总应该知道一些数学的特点。否则,说出了糊涂话来自己还不知道。陈景润被 批判了。他被帽子工厂看中了:修正主义苗子,安钻迷,白专道路典型,白痴,寄生 虫,剥削者。就有这样的糊涂话:这个人,研究（1+2 ）的问题。他搞的是ー套人们 莫名其妙的数学。让哥德巴赫猜想见鬼去吧!（1+2）有什么了不起! 1+2不等 于3吗?此人混进数学研究所,领了国家的工资,吃了人民的小米,研究什么1 +2 =3,什么玩意儿?！伪科学！	Chen Jingrun was born in Fujian in 1933. From the outset, his family circumstances offered none of life’s rose-colored radiance. His father, a postal clerk constantly on the move, refused to join the Kuomintang, a decision some colleagues mocked as a failure to adapt to the times. His mother, a gentle woman worn down by labor, gave birth to twelve children, of whom only six survived. Chen Jingrun was the third-born, with an elder brother and sister. In such a crowded household, children could not be cherished sons and daughters. Rather, they became burdens, surplus mouths and surplus lives. From the day he entered the world, Chen seemed fated to be unwelcome in it.
说这话的人才像白痴呢。	Chen Jingrun’s childhood held little joy. His mother worked from dawn to dusk, with no time left to show her children affection. By the time he was old enough to understand the world, war had erupted. Japanese forces had invaded Fujian Province, and he lived in a constant state of fear. His father was then serving as the director of a small postal branch in Sanming City, Sanyuan County, housed in an old temple deep in the mountains. The area had once been a revolutionary base, but by then the surrounding forests had grown desolate. Kuomintang bandits had massacred all the local men. None survived, not even the elderly. Only women remained, struggling to endure.
并不懂得数学的人说出这样的话,那是可以理解的,可是说这些话的人中间, 有的明明是懂得数学,而且是知道哥德巴赫猜想这道世界名题的。那么,这就是恶 意的诽谤了。权カ使人昏迷了;派性叫人发狂了。	Cloth was prohibitively expensive, and even grown girls often went bare-chested. After Fuzhou fell to enemy forces, waves of refugees fled into the mountains. Because aircraft rarely bombed the region, life there gradually regained a fragile calm, until a concentration camp was relocated nearby. At night, the crack of whips echoed through the darkness, punctuated by sporadic gunfire from executions. By morning, prisoners were marched out in shackles to perform forced labor, their figures gaunt and broken.
理解ー个人是很难的。理解一个数学家也不容易。至于理解一个恶意的诽谤 者却很容易,并不困难。只是陈景润发病了,他病重了。钢铁エ厂也来光顾了。陈 景润听着那些厌恶与侮辱他的,唾沫横飞的,听不清楚的言语。他茫然直视。他两 眼发黑,看不到什么了。他像发寒热ー样颤抖。ー阵阵刺痛的怀疑在他脑中旋转。 血痕印上他惨白的面颊。ー块青一块黑,ー种猝发的疾病临到他的身上。他眩晕, 他休克,ー个倒栽葱,从上空摔到地上。“资产阶级认为最革命的事件,实际上却是 最反革命的事件。果实落到了资产阶级脚下,但它不是从生命树上落下来,而是从 知善恶树上落下来的。”（马克思:《雾月十八日》ーニ）	Given his upbringing during a troubled time in history, Chen Jingrun's young heart suffered profound trauma. He was often overwhelmed by panic and confusion. There was no joy at home, and at elementary school, he was constantly bullied. He felt like an ugly duckling, yet somewhere within, he believed he possessed worth. It was only that his thin and frail body, his pitiful appearance, failed to win affection. He grew accustomed to being beaten, never pleading for mercy—only to be struck all the harder for his silence. Over time, he became increasingly resilient, his endurance quietly hardening into strength. Yet at the same time, Chen was overly sensitive, acutely aware of the cruel, predatory nature of the old society. This shaped him into an introverted person with a withdrawn nature. He devoted himself entirely to mathematics—not from compulsion, but from a deep and abiding passion. Much of his life was spent immersed in the pursuit of problems.
七	When Chen Jingrun entered junior high school, Jiangsu College relocated from a distant occupied area to the nearby mountains, and some of its professors began teaching part-time at the local school to support themselves as refugees. These teachers were highly educated. The Chinese language teacher was regarded as the most accomplished, and everyone admired him. Chen, however, had little interest in Chinese. He preferred his two mathematics and science teachers, who also took a liking to him and often spoke of “saving the country through science.”
台风的中心是安静的。	Although Chen did not believe that science alone could save the nation, he was convinced that it would be impossible to save the country without it—and especially without mathematics, which he considered indispensable to all matters. The discrimination he endured, the blows and kicks from peers, only deepened his devotion to mathematics. Algebraic equations, dry and tedious to the average eye, became a source of solace for Chen—his only joy.
过了一段时间,不知是多少天多少月,“专政队”的生活反倒平静无事了。而 旋卷在台风里面的人却焦灼着、奔忙着、谋划着、叫嚷着、战斗着,不吃不睡,狂热地 保护自己的派性,疯狂地攻击对方的派性。他们忙着打派仗,竟没有时间来顾及他 们的那些“专政”对象了。这时有一个老红军,主动出来担当了看守他们的任务。 实际是ー个热情的支持者,他保护了科学家们,还允许他们偷偷地看书。	At the age of thirteen, his mother died of tuberculosis. From then on, he missed his dear mother in dreams, even after his father remarried. His stepmother treated him even more coldly than his birth mother had.
待到工人宣传队进驻科学院各所以后,陈景润被释放了,可以回到他自己的小 房间里去住了。不但可以读书,也可以运算了。但是总有一些人不肯放过他。每 天,他们来敲敲门,来查查户ロ,弄得他心惊肉跳,不得安身。有一次,带来了克丝 钳子。存心不让他看书,把他房间里的电灯饺了下来,拿走了。还不够,把开关拉 线也剪断了。	After the victory in the War of Resistance against Japanese Aggression, the family returned to Fuzhou. Chen Jingrun enrolled at Sanyi Middle School, and after graduating, attended Yinghua Academy for high school. By chance, one of his mathematics teachers there had previously served as the director of the Department of Aeronautics at Tsinghua University.
于是黑暗降临他的心房。	III
但是他还得在黑暗中活下去啊,他买了一只煤油灯。又生怕煤油灯光外露,就 在窗子上糊了报纸。他挣扎着生活,简直不成样子。对搞工作的,扣他们エ资;搞 打砸抢的,反而有补贴。过了这样久心惊肉跳的生活,动辄得咎,他的神经极度衰 弱了。工作不能做,书又不敢读。エ宣队来问:为什么要搞1+1=2以及1+2=3 呢?他哭笑不得,张皇失措了。他语无伦次,不知道怎样对师傅们解说才能解释清 楚。工人同志觉得这个人奇怪。但是他还是给他们解释清楚。这（1 +1）（1 + 2） 只是ー个通俗化的说法,并不是日常所说的1+1和1+2。好像我们说ー个人是纸 老虎,并不就是老虎了。弄清楚了之后, 工人师傅也生气地说:那些人为什么要胡	The teacher was highly knowledgeable and tireless in his instruction. In class, he introduced students to many fascinating mathematical ideas. Even those who had little interest in the subject found themselves drawn in by his teaching, let alone those who already loved mathematics.
说?他们也热情支持他,并保护他了。	Mathematics is generally divided into two main branches: pure mathematics and applied mathematics. Pure mathematics focuses on numerical relationships and spatial forms, and within the study of numerical relationships, an important field that examines the properties of integers is called number theory. The 17th-century French mathematician Fermat is considered the founder of Western number theory, yet long before that, ancient China had already made significant contributions. The Zhoubi Suanjing, for instance, is the oldest surviving classical mathematical text, and the Sunzi Suanjing introduced a remainder theorem that later spread to the West and became known as Sun Zi's Theorem. Up until the Ming dynasty, China made substantial contributions to mathematics: in the 5th century, Zu Chongzhi calculated the value of pi more than a thousand years before the German mathematician Ludolph van Ceulen. In recognition, Soviet scientists later named a valley on the moon “Zu Chongzhi.” The second half of the 13th century marked the peak of ancient Chinese mathematics, when Qin Jiushao of the Southern Song dynasty wrote Mathematical Treatise in Nine Sections, describing methods for solving systems of linear equations—five hundred years before Euler. Around the same time, Zhu Shijie of the Yuan dynasty composed Jade Mirror of the Four Unknowns, which presented techniques for solving higher-order multivariable equations—four centuries before Bézout. After the Ming and Qing dynasties, however, China gradually fell behind. Yet the Chinese people have long demonstrated a natural aptitude for mathematics, and the nation retains its fertile ground for the cultivation of great mathematicians.
“九・ 一三”事件之后,大野心家已经演完了他的角色,下场遗臭万年去了。 陈景润听到这个传达之后,吃惊得说不出话来。这时,情况渐渐地好转。可是他却 越加成了惊弓之鸟。激烈的阶级斗争使他无所适从。唯一的心灵安慰从来就是数 学。他只好到数论的大高原上去隐居起来。现在也允许他这样做,继续向数学求 爱了。图书馆的研究员出身的管理员也是他的热情支持者。事实证明,热情的支 持者,人数众多。他们对他好,保护他。他被藏在ー个小书库的深深的角落里看 书。由于这些研究员的坚持,数学研究所继续订购世界各国的文献资料。这样几 年,也没有中断过,这是有功劳的。他阅读,他演算,他思考,情绪逐步地振作起来。 但是健康状况却越加恶化了,他从不说,他也不顾。他又投身于工作。白天在图书 馆的小书库一角,夜晚在煤油灯底下,他又在攀登,攀登,攀登了,他要找寻一条ー 步也不错的最近的登山之途,又是最好走的路程。	One day, this teacher decided to tell his high school students about a famous unsolved problem in number theory. He explained that when Peter the Great was building St. Petersburg, he brought together many leading European scientists, among them the Swiss mathematician Euler, who authored more than eight hundred works, and a German secondary school teacher named Goldbach, who was also a mathematician. In 1742, Goldbach observed that every large even number could be written as the sum of two prime numbers. He tested many even numbers and found the statement always to be true, but it still required proof. Since he could not prove it himself, he wrote to the renowned mathematician Euler to ask for assistance. Yet even Euler, until his death, could not solve it. Since then, this question has become one of the great challenges in the field of mathematics, drawing the efforts of thousands of mathematicians. For more than two hundred years, countless attempts have been made to prove the conjecture, but none has succeeded.
敬爱的周总理一直关心着科学院的工作,腾出手来排除帮派的干扰。半个月 之前,有一位周大姐被任命为数学研究所的政治部主任。由解析数论、代数数论等 学科组成的五学科室恢复了上下班的制度。还任命了支部书记,是个エ农出身的 基层老干部,当过第二野战军政治部的政治干事。	The classroom erupted with excitement. The students, like flowers newly in bloom, came alive, chatting and debating with enthusiasm. The teacher went on, “Mathematics is the queen of the natural sciences. Number theory forms her crown, and Goldbach’s conjecture is the pearl set within it.”
到职以后,书记就到处找陈景润。周大姐已经把她所了解的情况告诉了他。 但他找不到陈景润。他不在办公室里,办公室里还没有他的办公桌。他已经被人 忘记掉了。可是他们会了面,会面在图书馆小书库的ー个安静的角上。	All the students stared wide-eyed in amazement.
刚过国庆,十月的阳光普照。书记还只穿一件衬衣,衰弱的陈景润已经穿上 棉袄。	The teacher said, “You all know even and odd numbers, and you all know prime and composite numbers. We learned those back in third grade, didn't we? Easy, right? No—this problem is the hardest of all. If anyone could solve it, it would be incredible!”
“李书记,谢谢你,”陈景润说,他见人就谢。“很高兴,”他说了一连串的很高 兴,他ー见面就感到李书记可亲,“很高兴。”李书记,我很高兴,李书记,很高兴。	The students immediately burst into chatter.
李书记问他:“下班以后,下午五点半好不好?我到你屋去看看你。”	“What's so incredible about that?” one shouted. “We'll solve it! We can solve it!” they boasted, laughing and jostling each other.
陈景润想了一想就答应了 :“好,那好,那我下午就在楼门口等你,要不你会找 不到的。”	The teacher chuckled. “Really? Why, just last night I dreamed that one of you miraculously proved Goldbach's conjecture!”
“不,你不要等我,”李书记说,“怎么会找不到呢?找得到的。完全用不到 等的。”	The classroom burst into laughter.
但是陈景润固执地说:“我要等你,我在宿舍大楼门ロ等你。不然你找不到。 你找不到我就不好了。”	But Chen Jingrun didn't laugh. He, too, was shaken by the teacher's words, yet he couldn't bring himself to join in. If he did, the others would mock him with contempt. Since entering high school, he had become increasingly withdrawn. His classmates found him strange, unkempt, sickly-looking; thus, they ignored him. Some mocked him outright and shut him out. He became a solitary figure who was both isolated and introspective, a lone wolf without a pack.
果然下午他是在宿舍大楼门口等着的。他把李书记等到了,带着他上了三楼, 请进了一个小房间。小小房间,只有六平方米大小。这房间还缺了一只角。原来 下面二楼是个锅炉房。长方形的大烟囱从他的三楼房间中通过,切去了房间的六 分之一。房间是刀把形的。显然它的主人刚刚打扫过清理过这间房了,但还是不 太整洁。窗子三桶,糊了报纸,糊得很严实。尽管秋天的阳光非常明丽,屋内光线 暗淡得很。纱窗之上,是羊尾巴似的卷起来的窗纱。窗上缠着绳子,关不严,虫子 可以飞出飞进。李书记没有想到他住处这样不好。他坐到床上,说:“你床上还挺 干净!”	The next day, class resumed. Several eager students excitedly handed the teacher sheets of paper. They claimed they had already solved it, that they could prove Goldbach's conjecture, and in several different ways at that. “It's not that hard! We’ve worked it out!” they insisted.
“新买了床单。刚买来的床单,”陈景润说,“你要来看看我,我特地去买了床 单。”指着光亮雪白的蓝格子花纹的床单,“谢谢你,李书记,我很高兴,很久很久 了,没有人来看望……看望过我了。”他说,声音颤抖起来。这里面带着泪音。霎时 间李书记感到他被这声音震撼起来,满腔怒火燃烧。这个党的工作者从来没有这 样激动过。不像话,太不像话了!这房间里还没有桌子。六平方米的小屋,竟然空 如旷野。ー捆捆的稿纸从屋角两只麻袋中探头探脑地露出脸来。只有四叶暖气片 的暖气上放着ー只饭盒,ー堆药瓶,两只暖瓶。连ー只矮凳子也没有。怎么还有ー 只煤油灯?他发现了,原来房间里没有电灯。“怎么?”他问,“没有电灯?”	“I don’t believe you!” the teacher said, with a grin. “Just forget it!”
“不要灯,”他回答,“要灯不好。要灯麻烦。这栋大楼里,用电炉的人家很多, 电线负荷太重,常常要检查线路,一家家地都要查到。但是他们从来不查我。我没 有灯,也没有电线。要灯不好,要灯添麻烦了。”说着他凄然一笑。	“But we calculated everything—we have the answer!”
“可是你要做工作。没有灯,你怎么做工作?说是你工作得很好。”	“Come on, why waste your energy? You can give it up,” the teacher replied in amusement, still smiling. “I won't even look at those papers. Do you think it's that easy? You might as well try to ride a bicycle to the moon!”
“哪里哪里。我就在煤油灯下工作;那,ー样工作。”	The classroom roared boisterously again.
“桌子呢?你怎么没有桌子?”	Those students who hadn't handed in papers jeered at the few who had, stamping their feet and laughing until their sides hurt. Only Chen Jingrun didn't laugh. He knitted his brows tightly, excluded from all this joy.
陈景润随手把新床单连同褥子ー起翻了起来,露出了床板,指着说:“这不是? 这样也就可以工作了。”	The following year, the teacher returned to Tsinghua. His name was Shen Yuan, vice president of the Beijing Aeronautical Institute and chairman of the National Aeronautical Society. He had likely long forgotten those two mathematics classes, never realizing how deeply he was etched in the memory of his student, Chen Jingrun. Teachers, having taught many pupils, forget easily, but students often remember the teachers who shaped their youth.
李书记皱起了眉头,咬牙切齿了。他心中想着:“唔,竟有这样的事!在中关 村,在科学院呢。糟蹋人啊,糟蹋科学！被糟蹋成了这个状态。”ー边这样想,ー边 又指着羊尾巴似的窗纱问道,“你不用蚊帐?不怕蚊虫咬?”	IV
“晚上不开灯,蚊子不会进来。夏天我尽量不在房间里待着。现在蚊子少了。”	Fuzhou was liberated! At the time, Chen Jingrun was in his third year of high school. Unable to afford tuition, he stayed home and studied on his own during the first half of 1950. Although he never formally graduated, he was admitted to Xiamen University on the strength of equivalent academic credentials. That year, the university had only a Department of Mathematics and Physics. By his second year, a small mathematics group was formed with just four students, and by his third year, the group had grown into a full Mathematics Department—though it still consisted of the same four. Not only because of their outstanding academic performance but also because the country urgently needed trained specialists, the four graduated early and were immediately assigned jobs, receiving preferential treatment that others envied.
“给你灯,”李书记加重了语气说;接上线,再给你桌子,书架,好不好?”	In the autumn of 1953, Chen Jingrun was sent to Beijing to teach mathematics at No. X Middle School. It should have been a moment of great fulfillment, but it was not so.
“不好不好,不要不要,那不好,我不要,不……不……”	At Xiamen University, his days had been good ones. In his group and department, there were only four students, but also four professors and an assistant instructor to guide them. He absorbed knowledge hungrily, as though gathering nectar from a hundred blossoms to distill the honey of mathematics, fragrant and rich. His learning was remarkably fruitful. He roamed freely through the abstract realm, where everyone spoke the shared language of dx and dy, where heart spoke to heart and soul to soul.
李书记回到机关。他找到了比他自己早到オー个星期的办公室老张主任。主 任听他说话后,认为这一切不可能:“瞎说！怎么会没有灯呢?”李书记给他描绘了 小房间的寂寞风光。那些身上长刺头上长角的人把科学院搅得这样！立刻找来了 电エ。电エ马上去装灯。灯装上了,开关线也接上了。ー拉,灯亮了。陈景润已经	For three years, no one discriminated against him; no one scolded or struck him. Though he kept little contact with others, he lived golden years—wholly immersed in the ocean of mathematics. He had never imagined graduation would come so soon. At the thought of standing at a teacher's podium, facing dozens of sharp and curious—sometimes mischievous—eyes, he could not help but tremble with fear.
俯伏在ー张桌子之上,写起来了 〇	His conjecture was immediately proven correct. He was completely unsuited to teaching. While he was thin and weak, his students were all tall and robust. He was unskilled at speaking; even after only a few sentences, his throat would hurt. How he envied those sage and eloquent teachers. After class, returning to his room, he called himself an idiot, cursing himself more harshly than others ever did. He had never learned to care for himself and paid little attention to nutrition. Anxiety and strain took their toll, manifesting in illness. His fever climbed to 38 degrees Celsius. When he was sent to the hospital, several doctors diagnosed him with both pulmonary and peritoneal tuberculosis.
光明回到陈景润的心房。	That year, he was hospitalized six times and underwent three surgeries. Consequently, he couldn't teach well under these circumstances. Yet he didn't abandon his specialty. The Chinese Academy of Sciences had recently published Hua Luogeng's famous work, Additive Theory of Prime Numbers. As soon as it appeared on bookstore shelves, Chen Jingrun bought it. He dove right in. This was a profound work, proving difficult to master. Nevertheless, he studied it intensively. Even when hospitalized, he studied it secretly, avoiding the critical eyes of doctors and nurses, who advised him to focus on recovery. He thought then that, given his poor health, the school had little reason to welcome him.
〔他写着写着〕	He thought he might lose his job. What could he do about it? Fortunately, he lived frugally—so frugally that he didn't even buy a toothbrush. He never spent a penny carelessly and had saved nearly all his income. He steeled himself: if he were dismissed, he would simply return home and continue his mathematical research. Those few saved coins were his guarantee—his lifeline—for pursuing mathematics, which for him was life itself.
由（22 ）式及上式,当、很大时,有	As for what would happen when the savings ran out, he didn't know. That too was a hard problem—one without an answer. And later events confirmed it: his illness did not improve, and the middle school could no longer keep him.
MiW（8 + 24e）仁（logz）T	Around that time, the president of Xiamen University traveled to Beijing for a meeting at the Ministry of Education. During the visit, a leader from the middle school where Chen Jingrun taught voiced strong dissatisfaction, complaining bitterly: “This is the quality of an outstanding student from your institution?”
, ユ,し，矶"。	Wang Yanan—the president of Xiamen University and translator of Marx's Capital—was taken aback. He had always regarded Chen Jingrun as one of the university's finest students and firmly rejected the criticism. To him, the problem lay not with Chen but with the inappropriate assignment of his work. He promptly decided to bring Chen Jingrun back to Xiamen University.
ZÏÔVP1<Z3。2〈（言）2 ' Pli>2 '	When Chen Jingrun learned that he could return to the Mathematics Department at Xiamen University, his illness, curiously enough, began to improve. Wang Yanan, however, arranged for him to work at the university library—not to manage books, but to give him the freedom to devote himself entirely to mathematical research. True to his reputation as a critic of political economy, Wang Yanan understood not only the theory of value but also the value of human potential.
”〈南	Chen did not disappoint the president. He studied diligently, mastering Hua Luogeng's Additive Theory of Prime Numbers as well as the formidable Introduction to Number Theory.
由引理1,本引理得证。	Yet this kind of story was not without precedent.
引理8.设"是大偶数,则有	The senior mathematician and educator Xiong Qinglai—known as the pioneer who introduced modern mathematics to China—had once taught at Tsinghua University in Beijing. In the early 1930s, a young man who had completed only junior high school and could no longer afford to continue his studies began teaching himself mathematics. He sent a paper on the solutions of algebraic equations to Xiong Qinglai, who immediately recognized the author's extraordinary talent.
	Xiong invited the young man—Hua Luogeng—to join Tsinghua, arranging for him to work as a clerk in the Mathematics Department while allowing him to study independently and attend lectures. Later, Xiong sent Hua to the University of Cambridge in England. After completing his studies and returning to China, Xiong—then president of Yunnan University in Kunming—recommended Hua as a professor at the Southwest Associated University. Hua would later go abroad again, teaching at Princeton University and the University of Illinois. After the founding of the People's Republic of China, he returned home without hesitation and assumed leadership of the Institute of Mathematics at the Chinese Academy of Sciences.
c<3. 9404め	At Xiamen University Library, Chen Jingrun soon began writing specialized papers on number theory and sending them to the Institute of Mathematics at the Chinese Academy of Sciences. After reading them, Hua Luogeng immediately noticed Chen Jingrun's exceptional talent and recommended that he be appointed as a research intern at the institute. Just as Xiong Qinglai had once recognized Hua Luogeng's promise, Hua now discerned the same bright potential in Chen Jingrun.
（1。拿、）,。	At the end of 1956, Chen Jingrun once again journeyed from the southern coast to the capital, Beijing.
〔引理8的一句话,读作“设ル是ー个大偶数,则有奥米茄小于或等于3点 940MC,,除以括弧中的罗格%的平方!”请注意,这ー公式是解决哥德巴赫猜 想的（1 +2）证明的主要关键。〕	In the summer of 1957, the great mathematician Xiong Qinglai also returned to the capital from abroad. At that time, the young and the old gathered together—masters and rising stars alike assembled in one place. Among the renowned mathematicians were Xiong Qinglai, Hua Luogeng, Zhang Zongsui, Min Sihe, and Wu Wenjun, along with many other brilliant figures. A new generation of talents was also emerging—Lu Qikeng, Wan Zhexian, Wang Yuan, Yue Minyi, Wu Fang, and others—shining like the first light of dawn. And there were promising newcomers as well, such as Lu Ruling, Yang Le, and Zhang Guanghou, who had just entered Peking University to pursue their studies.
证。当・很大时,由引理5到引理7,我们有	In fields such as analytic number theory, algebraic number theory, function theory, functional analysis, and geometric topology, talent flourished in abundance—and now Chen Jingrun had joined their ranks. Every scholar shone with the brilliance of jade, each mind a polished gem. Winds gathered and clouds rose—the atmosphere was charged with vitality and purpose.
諡，ペ〈"がかmlog嘉	The conditions were ripe. Hua Luogeng made his plan: to strengthen applied mathematics, but also to advance toward that pearl in the crown—Goldbach's conjecture.
xïô <p] <ア耳 J 丁 3 力，(logt)log ミ	V
何等动人的ー页又一页篇页!这些是人类思维的花朵。这些是空谷幽兰、高 寒杜鹃、老林中的人参、冰山上的雪莲、绝顶上的灵芝、抽象思维的牡丹。这些数学 的公式也是ー种世界语言。学会这种语言就懂得它了。这里面贯穿着最严密的逻 辑和自然辩证法。它是在探索太阳系、银河系、河外系和宇宙的秘密,原子、电子、 粒子、层子的奥妙中产生的。但是能升登到这样高深的数学领域去的人,一般地 说,并不很多。	To understand Goldbach's conjecture, one needs only to recall the mathematics learned as early as third grade. The numbers 1, 2, 3, 4, 5—ones, tens, hundreds, thousands, ten-thousands—are called positive integers. Numbers that can be divided evenly by 2 are called even numbers; those that cannot are called odd numbers. Another type of number—2, 3, 5, 7, 11, 13, and so on—can be divided only by 1 and itself; these are called prime numbers. Numbers that can also be divided by other integers besides 1 and themselves—such as 4, 6, 8, 9, 10, and 12—are called composite numbers. If an integer can be divided by a prime number, that prime is called a prime factor of the integer. For example, 6 has two prime factors, 2 and 3, while 30 has three: 2, 3, and 5. For now, this much is enough.
且让我们这样稍稍窥视一下彼岸彼土。那里似有美丽多姿的白鹤在飞翔舞 蹈。你看那玉羽雪白,雪白得不沾一点尘土;而鹤顶鲜红,而且鹤眼也是鲜红的。 它瞬躅徘徊,ー飞千里。还有乐园鸟飞翔,有鸾凤和鸣,姣妙、娟丽,变态无穷。在 深邃的数学领域里,既散魂而荡目,迷不知其所之。	In 1742, Goldbach wrote to Euler and proposed that every even number not less than 6 could be expressed as the sum of two primes. For instance, 6 = 3 + 3, and 24 = 11 + 13, and so on. Mathematicians have verified this for even numbers up to 330 million, all of which satisfy the conjecture. But what about numbers far greater still? By conjecture, the statement should hold for them as well. Yet conjectures demand proof. This one, in particular, has proven extraordinarily difficult.
闵嗣鹤老师却能够品味它,欣赏它,观察它的崇高瑰丽。他当时说过:“陈景润 的工作,最近好极了。他已经把哥德巴赫猜想的那篇论文写出来了。我已经看到 了,写得极好。”	Throughout the eighteenth century, no one could prove it.
“你的论文写出了,”一位军代表问陈景润,“为什么不拿出来?”	Nor could anyone in the nineteenth century.
陈景润回答他:“正做正做,没有做完。”军代表说:“希望你早日完成。”	It was not until the 1920s, in the twentieth century, that real progress began. For a long time, mathematicians sought to show that every large even number could be written as the sum of two numbers with “not too many prime factors.” The idea was to create an ever-tighter encirclement—narrowing the range step by step—until one could finally prove Goldbach's claim: that every even number is the sum of two primes (1 + 1).
室里的领导老田对李书记说:“可以动员动员他,让他拿出来。但也不急。他 不拿出来,自然有他的道理的。”	In 1920, the Norwegian mathematician Brun, using an ancient technique known as the sieve method (a classical tool in number theory), proved that every sufficiently large even number can be expressed as the sum of two numbers, each having no more than nine prime factors. In other words, any large even number could be written as the sum of two numbers that were each the product of at most nine primes (9 + 9). This was an important milestone achieved through the sieve method. Still, the encirclement was far too wide and needed further tightening, and gradually, it was.
李书记问了问他,陈景润说:“有人还在骂我,说我不交论文是因为现在没有稿 费了,说是恢复了稿费我就会交了。”李书记追了他句:“谁这样说你?”他回答:“你 不要问了。谢谢你,你可别去问啊!问了我更麻烦了。没有稿费,谢天谢地。我不 要稿费。我压根儿也没有想到它。那个稿子我还在做。我确实没有做完。”	In 1924, the mathematician Rademacher proved (7+7); in 1932, Estermann proved (6+6); in 1938, Buchstab proved (5+5); and in 1940, he also proved (4+4). In 1956, Vinogradov established (3+3), and in 1958, the Chinese mathematician Wang Yuan proved (2+3). Step by step, the encirclement grew tighter, moving ever closer to (1+1). Yet all of these results shared a weakness: in none of them could either number be confirmed as prime.
九	As early as 1948, the Hungarian mathematician Rényi proposed another line of attack. He opened a new front, attempting to prove that every large even number can be written as the sum of one prime and another number with no more than six prime factors. He succeeded in proving (1+6).
“我确实还没有做完。我的论文是做完了,又是没有做完的。自从我到数学研 究所以来,在严师、名家和组织的培养、教育、熏陶下,我是一个劲儿钻研。怎么还 能干别的事?不这样怎么对得起党?在世界数学的数论方面三十多道难题中,我 攻下了六七道难题,推进了它们的解决。这是我的必不可少的锻炼和必不可少的 准备。然后我才能向哥德巴赫猜想挺进。为此,我已经耗尽了我的心血。	But after that, there was no progress for the next ten years.
“ー九六五年,我初步达到了（1 +2 ）。但是我的解答太复杂了,写了两百多页 的稿子。数学论文的要求是:（一）正确性,（二）简洁性。譬如从北京城里走到颐	In 1962, the Chinese mathematician Pan Chengdong, a lecturer at Shandong University, proved (1+5), moving the problem forward by one step; later that same year, Wang Yuan and Pan together established (1+4). In 1965, Buchstab, Vinogradov, and Bombieri all proved (1+3).
和园那样,可有许多条路,要选择一条最准确无错误,又最短最好的道路。我那个 长篇论文是没有错误,但走了远路,绕了点儿道,长达两百多页,也还没有发表。国 外没有承认它,也没有否认它,因为它没有发表。从那年到今天已经过去了七年。	Then, in May 1966, a brilliant signal flare lit up the mathematical sky—Chen Jingrun announced in Issue 17 of the Chinese Academy of Sciences journal Science Bulletin that he had proved (1+2).
“这个事是比较困难的,也是难于被人理解的。从学习外语来说,我是在中学 里就学了英语,在大学里学的俄语;在所里又自学了德语和法语。我勉强可以阅读 而且写写了。又自学了日语、意大利语和西班牙语,到了勉强可以阅读外国资料和 文献的程度。因而在借鉴国外的经验和成就时,可以从原文阅读,用不到等人翻译 出来了再读。这是必不可少的ー个条件。我必须检阅外国资料的尽可能的全部总 和,消化前人智慧的尽可能不缺的全部的果实。而后我才能在这样的基础上解答 (1 +2)这样的命题。	Since joining the Institute of Mathematics, the buds of Chen Jingrun's talent had begun to blossom in full. On problems such as lattice points in circles, lattice points in spheres, Waring's problem, and the three-dimensional divisor problem, he advanced and refined the work of both Chinese and foreign mathematicians. These achievements alone constituted a highly significant contribution.
“我的成果又必须表现在这样的ー篇论文中,虽然是专业性质的论文,文字是 比较简单的;尽管是相对地严密的,又必须是绝对地精确的。若干地方就是属于哲 学领域的了。所以我考虑了又考虑,计算了又计算,核对了又核对,改了又改,改个 没完。我不记得我究竟改了多少遍。科学的态度应当是最严格的,必须是最严 格的。	Once he had built a solid foundation, he turned to Goldbach's conjecture with astonishing perseverance. He forgot to eat or sleep, working day and night, lost in thought, probing deep mysteries, performing endless calculations. So completely absorbed in mathematics, he often seemed dazed. Once, he even walked into a tree and asked who had bumped into him.
“我知道我的病早已严重起来。我是病入膏肓了。细菌在吞噬我的肺腑内脏。 我的心力已到了衰竭的地步。我的身体确实是支持不了啦!唯独我的脑细胞是异 常得活跃,所以我的工作停不下来。我不能停止……”	He poured all his intelligence and reason into this problem and paid dearly for it. His eyes grew sunken, his cheeks flushed with tuberculosis, his throat ravaged by laryngitis that left him coughing incessantly. Swelling and pain in his abdomen became unbearable. Even when half-conscious, his mind still circled around numbers and symbols.
十	Step by step, he climbed the rugged paths of mathematics, each ascent laborious. On the high plateau of abstraction, he scaled sheer cliffs, falling and climbing again. Misunderstandings clouded his vision, and ignorant mockery rang in his ears. Yet he paid no attention, wasting no breath on argument and enduring humiliation in silence. Eating frost and drinking snow, every step forward exacted a heavy price.
ー九七三年二月,春节来临。	He gasped for breath, sweat pouring like rain, often feeling he could go no further—yet still he climbed, with his hands, with his fingernails. The struggle was grueling. Time and again, he climbed only to fall, until even iron shoes would have been worn through. People mocked his tattered footwear, so full of holes, they joked, they must at least keep him safe from athlete's foot.
早一天,数学研究所的周大姐说,佳节前后,要特别关心一下病号。她说:“那 些老八路的作风,那些过去部队里形成的作风,我们千万不能丢掉了。尤其像陈景 润那样的同志,要关心他,他很顽强。他病得起不来了,但又没有起不来的时候。 在任何情况下挣扎起来,他坚持工作。他为什么?他为谁?为他自己吗?为他自 己,早就不干了。不是,他是为人民,为党工作。我们要去慰问他。也要慰问单位 里所有的病人。”	He could no longer count how many times he had slipped, how many times he had nearly been crushed. Yet he never gave up. Each failure became a lesson; each setback was forged into the nylon ropes and iron ladders of his ascent. Failure became the mother of success; success itself was born from failure.
其实,外表看来魁梧,说话声音洪亮的周大姐自己也是ー个カ疾从公,患有心 脏病,应当受到慰问的人。	He crossed snow lines, reached icy peaks and modern glaciers, struggling ever more against the thin air. Again and again, avalanches buried his progress, ice blocked the mountain, yet he pressed on like a mountaineer conquering Everest—climbing, climbing, climbing.
大年初一早晨,周大姐和几个书记,包括李书记,一行数人,把头天买好了的苹 果、梨子装进ー些塑料网线袋子。若干袋子大家分头提了,然后举步出发,慰问病 人。他们先到陈景润那里。他住得最近。	Malicious slander and ridicule struck like storm winds and dark clouds, but warm encouragement cleared the skies, and the sun of goodwill gave him strength. Toward his goal, he persevered unyieldingly. He climbed past the first steep step only to face an even more forbidding precipice ahead. He thought only of climbing above thousand-foot abysses, through breathtaking vistas.
陈景润正从楼梯上走下来。大家招呼他。他很惊讶,来了这许多的领导同志。 周大姐说:“过春节,我们看你来了,你的病好点了吧?”李书记也说:“新年好,给你 贺新年。”陈景润说:“噢,今天是新年了啊?我很高兴,谢谢你们,谢谢你们。新年 好,你们好。”李书记说:“到你屋里去坐坐吧。”“不,不行,”陈景润说,“你没有先给 我打招呼,不能进去。”周大姐沉吟了一下,说:“好吧,我们就不去了。李书记,你 给他送水果上楼吧。我们还上别家去,你回头再赶上我们好了。”李书记说:“好。” 周大姐和陈景润握手,并祝他早日恢复健康,然后转过身走了。李书记把水果袋递 给陈景润说:“春节了,这是组织上送给你的。希望你在新的一年里,多给党做点エ 作。” “不要水果,不要水果。”陈景润推却了 , “我很好,我没有病,没有什么……这 点点病,呃……呃,谢谢你,我很高兴。”说着说着他收下了水果。李书记说:“上你 屋聊聊? ”他又张手拦住:“不,不要进屋了,你没有给我打招呼。”	Sheets of calculation paper piled up like drifting snow—formulas, symbols, and proofs covering the floor three feet deep, rising like mountains at his knees, blooming into ten thousand snow lotuses.
李书记说:“那好,我不上去了。你有什么事,随时告诉我。我也得去追上他 们,到别家去看望看望。”于是握手作别,他返身走,刚走两步,后面又叫:“李书记, 李书记!”陈景润又追过来,把水果袋子给了李书记,并说,“给你家的小孩吃吧。 我吃不了这多。我是不吃水果的。”李书记说:“这是组织上给你的,不过表示表 示,一点点的心意罢了。要你好好保养身体,可以更好地工作。你收下吧,吃不下, 你慢慢地吃吧。”	At last, he reached the path to the summit: the step of (1 + 2).
他默然收下了。他嚙着泪送李书记到大楼门口。李书记扬手走了,赶上了周 大姐他们的行列。陈景润望着李书记的背影,凝望着周大姐一行人的背影模糊地 消失在中关村路林荫道旁的切面铺子后面了。突然间,他激动万分。他回上楼,见 人就讲,并且没有人他也讲:“从来所领导没有把我当作病号对待,这是头一次;从 来没有人带了东西来看望我的病,这是头一次。”他举起了塑料袋,端详它,说,“这 是水果,我吃到了水果,这是头一次。”	He proved this proposition, writing a lengthy paper over two hundred pages thick.
他飞快地进了小屋,一下子把自己反锁在里面了。	Professor Min Sihe carefully read the original manuscript of Chen Jingrun's paper, checking and rechecking, verifying again and again. At last, he confirmed that Chen Jingrun's proof was correct and reliable. He told Chen that the previous year others had proved (1+3) using powerful electronic computers, but Chen had proven (1+2) relying solely on his own calculations. No wonder the paper was so long. Accordingly, he suggested that it be simplified.
他没有再出来。直到春节过去了,头ー天上班,陈景润把ー叠手稿交给了李书 记,说:	The “reference [10]” cited at the end of the first section of this account refers to Chen Jingrun's brief announcement in Science Bulletin, which presented only the result, without the complete proof. At that time, he was still revising the full manuscript. But just then, Chen Jingrun was suddenly swept into the vast, tumultuous waves of political revolution. The surging tide struck at all ideologies of the exploiting class. The unprecedented Cultural Revolution, like a series of spiritual atomic and hydrogen bomb tests, detonated again and again across the land of China.
“这是我的论文。我把它交给党。”	VI
李书记看看他,又轻声问他:“是那个（1+2 ）?”	The “Cultural Revolution” launched by the proletarian class was also a great political revolution; it was unprecedented in scope and passion. Never before in human history had there been such a vast mass movement. A full quarter of humanity, regardless of gender or age, was mobilized. This magnificent upheaval swept together workers, peasants, soldiers, the laboring masses, and intellectuals—saints and devils alike. Accusing and being accused, exposing and being exposed, criticizing and being criticized: China entered a state of “civil war.”
“是的,闵老师已看过,不会有错误的。”陈景润说。	Everywhere there was organized fervor, directed combat, and orderly chaos. The proletarian revolution was relentless in its self-criticism—victory followed by reversal, reversal followed by new victory. It took seemingly completed tasks and redid them again and again, each time striving for greater perfection. It sought out its own weaknesses, shortcomings, and errors without mercy.
数学研究所立即组织了一次小型的学术报告会。十几位专家,听了陈景润的 报告,一致给以高度评价。然后,数学研究所业务处将他的论文上报院部	As Marx suggested, revolution drives the enemy back until there is no ground left to yield. Then, like the fabled leap on Rhodes, it acts in the present with decisive force, crushing its foe and rejoicing in the rose garden.
十yi	Scenes flashed by like wind and lightning, shaking the earth. Drama after drama unfolded—filled with joy, anger, sorrow, and ecstasy; partings and reunions that stirred hearts and souls. Character after character took the stage: some broke their halberds and fell in the sand, meeting the fate they deserved; the “four great families” vanished like a dream of the Red Chamber; some bloomed like epiphyllums, withering as swiftly as they appeared. Yet there were also pines and cypresses, evergreen even in death, whose spirits stood higher than Mount Tai, their noble essence enduring.
的证明。	Some were heroes, forged in struggle and spirit like the twin swords of Ganjiang and Moye, tempered by a thousand blows, silent as a bell when struck, yet sharp enough to cut iron as if it were clay.
完全类似的方法可得到定理2的证明。	Page after page of history was written, and in time, the great rights and wrongs received their due judgment. Affirmation—negation—negation of the negation. Makeup fades; it must peel away. The falsely accused, in the end, will be vindicated. Seeds once planted will bear fruit: what is sown will one day be reaped.
以上就是陈景润的著名论文《大偶数表为ー个素数及ー个不超过二个素数的 乘积之和》的“（三）结果” 〇作为结果的定理就是那个“陈氏定理” 〇	Then came the reckoning. Astronomy and geography had to be tested; physics and chemistry had to be tested; biology had to be tested—and mathematics, too, had to be tested.
四月中的一天,中国科学院在三里河工人俱乐部召开全院党员干部大会。武 衡同志在会上做报告。他说到数学研究所一位中级的研究员做出了世界水平的重 大成果。当时没说人名,听到了,还不知说谁。李书记在座中,捅了一下旁边的人。 “干什么?”那人说?他问:“你听到没有?”“怎么啦?”那人又说。“这活儿是陈景润 做出来的啊!”“噢?还这么重要?”那人说。“这是世界名题。真不简单!”	Chen Jingrun endured the harshest trials of the proletarian Cultural Revolution. Veteran mathematicians were struck down; even the middle-aged and young mathematicians could not escape. The once-solemn Academy of Sciences fell into chaos, its bustling laboratories turned cold and silent. Days and nights alike were filled with endless debate and fierce struggle. Words gave way to blows; fists replaced tongues.
第二天,新华社记者来访。他见到了陈景润,谈了话,进他房间看了看。回去 就写出ー篇报道,立即在内部刊物上发表。其中,说到了陈景润的经历,他刻苦钻 研的精神,重大的科研成果以及他现在还住在ー间烟熏火烤的小房间里。生活条 件很差!疾病严重!！生命垂危!！！	The Cultural Revolution was like a great sieve—everything had to be shaken through it. The Academy, too, was subjected to this sieve: what was meant to be sifted out would be removed; what was not could never be forced through.
伟大领袖和导师毛主席看到了这篇报道,立即做出了指示。	In earlier years, some had argued that scientific workers should be allowed to settle down to their work with peace of mind—immersing themselves in scholarship and devoting themselves wholly to their profession. But during the Cultural Revolution, this view was condemned as a bourgeois line of scientific research: “focus, immerse, absorb.” Chen Jingrun was singled out as a typical example. Indeed, he spent his days wholly absorbed in study. He cared little for politics, though he had taken part in every political movement. To him, the simple truth that the Communist Party was good and the Kuomintang bad was self-evident. A mathematician's logic is hard as steel, and his convictions were firm. He had committed no political errors. In understanding and belief, Chen Jingrun remained unsullied, pure as a crane. A crane's white feathers cannot be stained; though its crown is bright red, its eyes, too, are red, perhaps from long nights without sleep. Chen had gone to factories to labor and had also applied mathematics to practical production, even while pursuing number theory, the most abstract of theoretical sciences. Yet if he himself paid little attention to politics, politics inevitably turned its attention to him and subjected him to harsh criticism. Light criticism would not move him; only by shaking him, it was believed, could he be made to “care about the political line.” In this logic, criticism must not fear excess, for to straighten what is bent, one must first overcorrect. But could a single act of criticism turn a loyal scholar into an enemy of the people?
当天深夜,武衡同志走进了陈景润的小房间。	Well-intentioned misunderstandings can be clarified, and ignorant mockery can be forgiven. But to pass judgment on a mathematician, one should at least have some understanding of mathematics itself; otherwise, one merely spreads confusion without realizing it.
他立即被送进医院,由首都医院内科主任和卫生部一位副部长给他做了全面 的身体检查。他患有多种疾病。他们要他立即住院疗养,他不肯。于是,向他传达 了毛主席的指示。	Chen Jingrun soon became a target of denunciation. He was branded with cruel nicknames from the “label factory,” described as a revisionist seedling, focus-delve-absorb type, typical of the white-expert path, idiot, parasite, exploiter.
他ー共住院一年半。	Some even made remarks so absurd they bordered on the ridiculous: “This man studies the (1+2) problem. He's doing a kind of mathematics that nobody can understand. Let Goldbach's conjecture go to hell! What's so great about (1+2)? Doesn't 1+2 equal 3? This man snuck into the Mathematics Institute, lives off the state's salary, eats the people's grain, and spends his time on some 1+2=3 nonsense. What rubbish! Pseudo-science!”
在住院期间,敬爱的周总理曾亲自和华国锋副总理安排了陈景润的全国人民 代表席位。在第四届全国人民代表大会上,陈景润见到了周总理,并和总理在ー个 小组里开会。人代会期间,当他得知总理的病时,当场哭了起来,几夜睡不着觉。 大会后,他仍回医院治疗。	The person who said this was little more than a fool.
当他出院的时候,医院的诊断书上写着:	From those who did not understand mathematics, such words were perhaps excusable. But among those making these remarks were some who clearly did know mathematics—and who knew perfectly well that Goldbach's conjecture was a world-famous problem. From them, it was nothing less than deliberate slander. Power had clouded judgment, and factionalism had driven people mad.
“经住院治疗后,一般情况较好。精神改善;体温正常。体重增加十斤;饮食睡 眠好转。腹痛腹胀消失;二肺未见活动性病灶。心电图正常;脑电图正常。肝肾功 能正常;血沉及血象正常。”	Understanding a person is difficult; understanding a mathematician is no easier. But understanding a malicious slanderer—that is all too simple. By then, Chen Jingrun had fallen gravely ill. Even the steel factory came to “visit.” He listened as they hurled their vile insults, words spattered with flying spittle and incoherent rage. His gaze went blank; darkness clouded his eyes until he could see nothing. His body trembled as if struck by fever and chills. Piercing waves of doubt surged through his mind. Red streaks flared across his pale face, blotched with blue and black. Then the illness struck in full—he grew dizzy, his thoughts blurred, and he collapsed headfirst to the ground.
关于他的工作和健康,华国锋也非常关怀,并亲自做过几次批示。	As Marx wrote in Chapter 12 of The Eighteenth Brumaire, what the bourgeoisie considers the most revolutionary event is actually the most counter-revolutionary event. The fruit fell at the bourgeoisie's feet, but it did not fall from the tree of life—it fell from the tree of the knowledge of good and evil.
早在他的论文发表时,西方记者迅即获悉,电讯传遍全球。国际上的反响非常 强烈。英国数学家哈勃斯丹和西德数学家李希特的著作《筛法》正在印刷所校印。 他们见到了陈景润的论文立即要求暂不付印,并在这部书里加添了一章,第十ー 章:“陈氏定理。”他们誉之为筛法的“光辉的顶点”。在国外的数学出版物上,诸如 “杰出的成就”“辉煌的定理”等等,不胜枚举。ー个英国数学家给他的信里还说, “你移动了群山”！	VII
真是愚公一般的精神啊!	The center of a typhoon is quiet.
或问:这个陈氏定理有什么用处呢?它在哪些范围内有用呢?	After some time, no one could say how many days or months, life under the control of the so-called “dictatorship team,” a group tasked with enforcing proletarian authority over intellectuals, settled into an uneasy calm. Outside, the storm still raged: people plotted and shouted, fought and accused, neglecting food and sleep as they feverishly defended their factions and attacked others. But those confined under the “dictatorship team” were gradually forgotten. The energy of factional struggle left no one with time or will to notice them.
大凡科学成就有这样两种:ー种是经济价值明显,可以用多少万、多少亿人民 币来精确地计算出价值来的,叫作“有价之宝”；另ー种成就是在宏观世界、微观世 界、宇宙天体、基本粒子、经济建设、国防科研、自然科学、辩证唯物主义哲学等等等 等之中有这种那种作用,其经济价值无从估计、无法估计,没有数字可能计算的,叫 作“无价之宝”,例如,这个陈氏定理就是。	Amid this atmosphere of neglect and turmoil, an old Red Army veteran volunteered to guard the scientists. In truth, he was a quiet sympathizer who protected them, even allowing them to read in secret.
现在,离开皇冠上的明珠,只有一步之遥了。	When the worker propaganda teams later entered the institutes of the Academy of Sciences, Chen Jingrun had been released and permitted to return to his small room. There, he could not only read but also begin to calculate again. Yet peace never lasted long. Each day, someone would come knocking, checking household registrations, asking questions, keeping him perpetually on edge.
但这是最难的ー步。且看明珠归于谁之手吧!	Once, they arrived with wire cutters. Determined to stop him from reading, they cut the wire to the light in his room and carried the fixture away. Still unsatisfied, they went further and severed the switch cord itself.
十二	Darkness fell, not only upon his room, but upon his heart.
陈景润曾经是ー个传奇式的人物。关于他,传说纷纭,莫衷ー是。有善意的误 解、无知的嘲讽、恶意的诽谤、热情的支持,都可以使得这个人扭曲、变形、砸烂或扩 张放大。理解人不容易;理解这个数学家更难。他特殊敏感、过于早熟、极为神经 质、思想高度集中。外来和自我的肉体与精神的折磨和迫害使得他试图逃出于世 界之外。他相当成功地逃避在纯数学之中,但还是藏匿不了。纯数学毕竟是非常 现实的材料的反映。“这些材料以极度抽象的形式出现,这只能在表面上掩盖它起源于外部世界的事实。”（恩格斯）	But he still had to live on in the darkness. He bought a kerosene lamp, and, afraid its light would show through, he pasted newspapers over the windows. He struggled on in wretched conditions. Those who worked had their wages docked, while those who took part in smashing and looting were given subsidies. After living in constant fear for so long, walking on eggshells, his nerves grew fragile. He could not work and dared not even read.
陈景润通过数学的道路,认识了客观世界的必然 规律。他在诚实的数学探索中,逐步地接受了辩证唯物论的世界观。没有一定的 世界观转变,没有科学院这样的集体和党的关怀,他不可能对哥德巴赫猜想做出这 辉煌贡献。被冷酷地逐出世界的人,被热烈的生命召唤了回来。帮派体系打击迫 害,更显出党的恩惠温暖。冲击对于他好像是坏事;也是好事,他得到了锻炼而成 长了。病人恢复了健康,畸零人成了正常人,正直的人已成为政治的人,多余的人, 为国增了光。他进步显著,他坚定抗击了“四人帮”对他的威胁与利诱。无所不用 其极地威胁他诬陷邓副主席,他不屈!许以高官厚禄,利诱他向人妖效忠,他不动! 真正不简单!数学家的逻辑像钢铁ー样坚硬!今后,可以信得过,他不会放松了自 己世界观的继续改造。他生下来的时候,并没有玫瑰花,他反而取得成绩。而现在 呢?应有所警惕了呢,当美丽的玫瑰花朵微笑时。	Then the worker propaganda team came to question him: “Why are you engaged in 1+1=2 and 1+2=3?”
（原载《人民文学》1978年第1期）	He didn't know whether to laugh or cry. Flustered and confused, he stammered, unable to explain himself clearly to his inquisitors. The workers found him strange. At last, he managed to clarify: the “(1+1)” and “(1+2)” were merely shorthand expressions, not the 1+1 or 1+2 of everyday arithmetic. Just as calling someone a “paper tiger” doesn't mean an actual tiger, his formulas were metaphorical, not literal. Once they understood, the workers grew indignant at those who had spread such nonsense about him, and from then on, they supported and protected him with genuine warmth.
Master,直译是船长或主人。那么,对他,贝汉廷,怎样译更确切呢?	After the “September 13 Incident,” when Lin Biao, Mao Zedong's once-designated successor, died in a plane crash while allegedly fleeing after a failed coup attempt, the political tide began to shift. The atmosphere of the Cultural Revolution slowly began to ease. When the news first broke, Chen Jingrun was so stunned that he could not speak. Though the situation gradually improved, he remained nervous and watchful, like a bird startled by the twang of a bow. The relentless years of class struggle had left him bewildered. His only refuge had always been mathematics, and now he was once again permitted to retreat into the boundless plateau of number theory.
我站在“汉川号”的驾驶台甲板上凭栏远眺,深深地思索着。海风迎面扑来, 新鲜而又湿润。远处,是神秘莫测的大海;近处,海鸥在我的脚下飞翔……	The librarian at the Institute of Mathematics, himself a former researcher, became one of Chen Jingrun's strongest supporters. In fact, there were several such allies who quietly looked out for him. Hidden away in a small corner of the institute's library stacks, he could finally read in peace. Thanks to the persistence of these researchers, the Mathematics Institute continued ordering foreign journals and academic publications year after year, a small but vital act of dedication. He read, calculated, and reflected; gradually, his spirits lifted. Yet his health continued to decline. He never mentioned it, never complained, but once again threw himself into his work. By day he labored in a quiet corner of the library, and at night, under the dim glow of a kerosene lamp, he climbed and climbed again, always searching for the mathematical path most direct, most certain, and least prone to error.
冈，才,在和海员们的谈话中,有什么搅动了我的心,为了掩饰我的泪水,我オ离 开船舱。但现在,在这蓝天与大海之间,我仍然不能平静,思绪的波涛追逐着海水, 去得很远很远……	Premier Zhou Enlai had long cared deeply about the work of the Academy of Sciences and made every effort to reduce factional interference. About half a month earlier, a woman surnamed Zhou had been appointed the director of the Institute of Mathematics' Political Department. The institute's five academic divisions, including analytic and algebraic number theory, soon resumed regular operations. A new Party branch secretary was also appointed, a veteran grassroots cadre from a worker-peasant background who had previously served as a political officer in the Second Field Army of the People's Liberation Army.
不知怎么,我ー下子离开主题,忽然想起二十多年前我给小读者写的一首诗, 告诉他们什么叫作海员。	After assuming his post, the secretary searched everywhere for Chen Jingrun. Sister Zhou had already briefed him on the situation, but Chen was nowhere to be found. He had no office, not even a desk. It seemed he had been completely forgotten. Finally, the secretary found him, in a quiet corner of the institute's small library repository.
我不禁嚙泪而笑了。那时我是那样年轻,在生活的海洋里几乎未经沉浮,我懂 得海员吗?那时的小读者今天应该也是三十多岁的人了,他们怕也有自己的孩子 了。经历过十多年的狂飙巨浪,他们还像儿时那样天真地向往海洋吗?天真,也许 是消失了,但向往ーー还应该向往。那么,就让我再给他们讲ー个海员的故事吧!	Just after National Day, with October sunshine shining everywhere, Secretary Li wore only a light shirt, while the frail Chen Jingrun was already wrapped in a padded jacket.
讲ー个海员,ー个水手,ー个船长,ー个master的真实的故事吧	“Thank you, Secretary Li,” Chen Jingrun said, his voice trembling. He repeated his gratitude again and again, unable to hide his relief at meeting someone so approachable.